economic growth on the EU and the US markets” “Relationship between credit spreads, equities and Master Thesis

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Master Thesis

“Relationship between credit spreads, equities and

economic growth on the EU and the US markets”

By Krasimir Hristov

University of Groningen

Faculty of Economics and Business

MSc Finance

Author: Krasimir Hristov Student number: S2677067 Supervisor: Mr. Richard Klijnstra

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1 ABSTRACT

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In today’s modern economy one of the most important questions that investors face is how to allocate their funds efficiently across different asset classes and be able to time their investments. Therefore, a deep understanding of the relationships between these different asset classes is a crucial component of every sound investment strategy. The formulation of investment strategy involves investors adopting a structural approach trough which important decisions have to be made.

The process of constructing the investment portfolio can be described with the following steps according to Sortino, Van der Meer, Platinga, Salomons, and Boonstra (2015):

- objectives of the investment strategy are formulated keeping into account the risk profile and risk appetite of investors;

- based on these objectives, preferences and constraints regarding the asset allocation are considered;

- an outlook for future economic trends is formed;

- the investment strategy is formulated. At this step investors consider their Strategic Asset Allocation (SAA) which is the initial allocation of funds between different asset classes such as stocks, bonds, commodities, real estate and cash. This allocation reflects the long-term expectations of investors about future performance among the different asset classes during the economic cycle developments;

- the final stage is the execution of the strategy and risk monitoring and management of the portfolio. For the purposes of allocating funds more effectively investors consider at this stage the Tactical Asset Allocation (TAA). This allocation is focused on the short term and the main assumption behind it is that markets trade in cycles and the investors are able to time these cycles by allocating their funds to the asset class that performs best in each part of the cycle. This allocation can deviate from the SAA for some periods of time;

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will perform best given the current part of the economic cycle. Therefore, understanding the relationships between these asset classes may help investors in their quest to time the cycles of asset returns and economic developments.

A very important question that is central to this research and will help in solving the

outlined issues above is whether the changes in credit spread can predict equity returns. If this is the case indeed investors can be more efficient in their TAA and reap great benefits for their portfolios.

Another important research question that this study answers is whether the changes in credit spread can be used as an indicator for future real economic output. The answer to

this question is crucial for investors as well as for economists and monetary policy decision making authorities and can help to predict future economic developments.

The main contribution of this paper to existing theory lies in the fact that the relationship between credit spreads and equities, to the best of my knowledge, was not examined before on the EU market (some literature is available for the US market). As far as the relation between credit spreads and real economic output is concerned, there are existing papers on the matter that examine the relationship only on the US market. What this research contributes to existing theory is the fact that its focus (for both research questions) is on the European and the US markets. Also in this research the excess corporate bond returns are used as proxy for the credit spread developments.

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5 2. Theoretical framework

In order to understand the predictive power of the credit spread a thorough understanding of concepts such as term structure of interest rates and the determinants of credit spreads is required. Therefore, in this section I discuss the most relevant concepts regarding credit spreads and also make a review of existing literature on the research questions outlined above.

2.1 Interest rates and yield curves

This section goes into detail in the definition of credit spread using the term structure of interest rates. The first step in defining an interest rate on every credit instrument is the definition of the risk-free interest rate. This rate is characterized as default-free and measures the return that investors can obtain with certainty by purchasing the risk-free asset. When it comes to calculating the risk-free rate academics and practitioners have applied different approaches. One of the most common methods to obtain this rate is to use the yield on different government bonds. In practice the most common used risk-free benchmarks are the German Bunds and the Treasury bills. Government bonds have different rates depending on the maturity of the securities. Therefore, Koller, Goedhart, and Wessels (2005) suggest using as risk-free benchmark the rates on government bonds that match the maturity of the cash flow stream that is expected to be generated from the debt instrument.

Another method that can be used in determining the risk-free rate is to use the “London Interbank Offered Rate” (LIBOR). Using the LIBOR curve, however, has some problems compared to using government bonds yield. One of those problems is the fact that observations of this rate are possible up to one year of maturity, but this can be circumvented by using swap rates to extend the LIBOR curve.

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credit ratings (AA or above) borrow from each other. This curve is typically higher than the government curve and is closely monitored by professionals and used as an indicator of what is happening at the financial markets. The third group of yield curves is the corporate curves, which are constructed from the yields of fixed income instruments issued from corporations. These corporations have a lower creditworthiness than governments and large banks so this curve lies above both government and LIBOR curves.

For the purposes of this research the risk-free rates used are the German government bond rates for the EU market and Treasury yields for the US market. The reasons for choosing these particular rates instead of LIBOR rate as risk-free benchmark are complex. Firstly, all existing theory on the matter, as discussed below, uses these rates as a proxy for the return on the risk-free asset. Another reason to avoid using LIBOR rates is the current evidence from investigations of financial regulators in the US and the UK that some banks manipulated this rate. Therefore any inferences made using LIBOR curves would be misleading because the risk-free rate would not be set by market forces, but from some exogenous forces that cannot be accounted for in the model. Last but not least, LIBOR rate is not completely risk-free. The spread between LIBOR and government curves contains a compensation for systematic risk.

2.2 Credit spread definition and discussion about its predictive powers

This section defines the credit spread and goes into detail about the informational content of the credit spread that is the basis for its predictive power.

The difference between the corporate and government/LIBOR curves is referred to as the credit spread. In this paper the term credit spread is used to describe exactly the spread over the government curve unless it is explicitly stated otherwise. It is common for corporate yields on bonds to be quoted on basis points (bps) over the relevant risk-free curve. In order to understand the predictive properties of this credit spread it is first useful to understand what information is embedded in it.

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What they find is that after 1980 such relationship does not hold at all at the US market. Then using a simple multiple regression Friedman and Kuttner (1989) reached the conclusion that the above mentioned credit spread contains valuable information regarding the real economic output and it is significant regardless of sample and inclusion of other variables in the equation.

Stock and Watson (1989) also confirmed that finding in their research on the US market and showed that the 6m Commercial paper versus 6m government bonds spread was able to outperform almost every other variable as an indicator for business cycle.

The explanation behind these findings provided by Friedman and Kuttner (1989) was that the Commercial paper – treasuries spread contained information about the default probabilities of companies and embedded the expectations of investors about the future economic prospects of companies.

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requires large minimum investments so most investors shift their funds to Treasury bills. This in fact lowers the interest rate on these bills relative to Commercial paper and widens the spread. Of course large investors and banks that do not suffer from the minimum investment constraint could just sell off their Treasuries to offset this shift in funds in the economy. Even though to some extent this can happen, Cook (1980) argues in the same article that Treasuries are valuable to these investors because they can be used as collateral and also for satisfying capital adequacy requirements.

A theory that is important to be discussed here is the theory of Credit Cycles. According to a report written by a team of CITI Bank analysts (14 August 2014) there are four credit phases identifiable and the full cycle lasts about 5 years.1 In the first phase the credit conditions begin to loosen up due to deleveraging by companies. This loosening is provoked by the fact that companies during the economic downturn start reorganizing their balance sheets and make them more attractive for creditors. In this phase the pressure on company profits is still high so equities continue to perform weak. The second phase is characterized by the end of equities’ bear market. In the meantime the credit bull market accelerates since increased cash flows have beneficial impact on balance sheet of companies. The third phase in the credit cycle begins when the credit bull market ends. Companies start to invest too much because of increased risk appetite and because of naive extrapolation of strong recent performance too far in the future. CEOs use debt excessively in order to engage in shareholder friendly actions. At this time investors begin to realize the sub-optimal increase in leverage in companies’ balance sheets and raise their assessment of default probabilities. Rising inflation also causes fears that a tight monetary policy might be imposed by regulators. Therefore spreads begin to widen but equities continue their rally. The fourth phase is characterized as a pure bear market – equities and credits decline together. The worsening balance sheets put pressure on companies’ profits and default probabilities increase substantially. The best performing asset classes at this stage are cash and government bonds.

Bernanke (1990) in the above mentioned article measures, among other variables, the effect of the spread between 6m Commercial paper and 6m Treasuries and the spread between 10y Commercial paper and 10y Treasuries on the real economic output at the US market. He

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concludes that the 6m spread was the best predictor followed by the long-term spread. His findings also confirmed the hypotheses that the credit spread contains information about the stance of monetary policy and to some weaker extent the default risk expectations of investors.

Later Friedman and Kuttner (1993) go into further detail in their article about why this spread predicts real economic activity. In order to be able to answer this question they decompose the observed spread “…into a component that covaries directly with the general level of interest rates, a component directly representing the variation over time in the perceived risk of default on commercial paper, and a component capturing other influences that may or may not be related to the business cycle” (Friedman and Kuttner, 1993, pp 214). Such component that may or may not be related to the economic cycle according to the authors is the fact that Treasury bills are tax exempt while the commercial paper is not. They find out that the credit spread indeed embedded in itself information about the perceived default risk, the monetary policy stance and the changing cash requirements of investors during the economic cycle. The authors argue that taxes are highly unlikely to be changed according to the business cycle, so the high forecasting powers of the spread must come from the difference in liquidity and default risk between the two securities.

Another interesting finding from this paper is the fact that the credit spread widened immediately prior to recessions and remained wider during recessions. A notable example when this was not the case is the recession of 1990 which this spread failed to predict. Friedman and Kuttner (1998) present two different not mutually exclusive explanations for that failure. The authors found out that the 1990-1991 recession was unusual in the sense that it was not related with tight monetary policy. Also the credit spread was affected by a change in the quantities of assets in the market portfolio such as commercial paper, bank deposits and Treasury bills. These changes were not triggered by the business cycle. The authors also found that there was no evidence that this failure can be attributed to the fact that Commercial paper and Treasury notes have become perfect substitutes. Therefore, their ability to forecast real economic output is not impaired.

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and the default risk expectations of market agents. Also the short-term spread is the best predictor but longer term spreads perform reasonably well as forecasters.

2.3 Credit spreads and relationship with equity returns

In order to understand fully the relationship between credit spreads and equity returns, first the common factors that drive equity and bond returns have to be examined. In their article Campbell and Ammer (1993) argue that the excess stock and bond returns contain information about “…changes in expectations of future stock dividends, inflation, short-term interest rates and excess stock and bond returns” (Campbell and Ammer, 1993, pp 3). One of their findings is that excess stock returns indeed react to future expectations of excess stock returns. The changes in interest rates are not important determinant in the long-term excess return of stocks. As far as bonds are concerned, the authors suggest that future inflation expectations affect negatively the excess bond returns and positive inflation is associated with decline in the credit spread. They also find out that bonds and stock covary negatively because positive inflation drives the stock market up but the bond market down.

Bharma, Kuehn, and Strebulaev (2010) in their article argue that there is a link between equity risk premium puzzle and the credit risk puzzle because of the ability of credit spreads to predict stock returns.2 Based on the understanding that credit spreads contain information about default probabilities they develop a model that forecasts the term structure of default probabilities accurately and helps in pricing bonds and equities because equity premiums take into account default probabilities also.

Chen, Roll, and Ross (1986) in their article support the view that stock prices are moved generally by changes in industrial production, changes in risk premium (higher default probabilities result in a higher premium and vice versa) and twists in the yield curve. These twists also measured the default probability. The authors use the spread between yields of high and low graded bonds in order to account for the change in risk premiums for equities. Their argument follows from existing finance theory – when this particular spread is low the expectations for deterioration in creditworthiness of companies are also low so the risk premium should be adjusted downwards. Keim and Stambaugh (1986) confirm these findings

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and also argue that return differences of bonds are likely to contain information about the changes of the expected risk premiums and thus affect equities.

Campbell (1987) in his article argues that the state of the term structure of interest rates predicts stock returns. For a discussion about term structures of interest rates please refer to section 2.1 in this paper. He also found out that excess returns over the risk-free rate on assets such as bonds have explanatory power with regard to excess returns generated by equities. The fact that stock and bond returns contain a maturity premium was examined by Fama and French (1989). The expected returns on these asset classes also contain a risk premium according to the authors and this premium is related to the expected development of business conditions. In their study they define the so-called default spread which is the spread between the yield of a market portfolio of corporate bonds and the yield of AAA bonds, which are essentially US Treasuries and very large banks. The authors found out that this spread widened during economic recessions and tightened when the economy was strong. Another finding was that the dividend yield of equities is highly correlated with that particular spread. Therefore, when conditions are poor the expected returns of stocks and bonds must be high and vice versa. If this line of argument is extended, it is easy to see that when the realized excess returns on corporate bonds are negative this will imply a widening of the credit spread because of deteriorating economic conditions. Fama and French (1993) in their article continue their research on common risk factors in the returns on stocks and bonds. They identify five common risk factors: three equity related - market, firm size, book-to-market and two bond related – maturity and default risks. The authors found evidence that the three stock market factors cannot be used to forecast the returns on government and corporate bonds, but that the bond and the stock markets are linked through the two bond market factors. Furthermore Whitelaw (1994) in his article found that the Commercial paper – Treasury yield spread can explain the volatility of equity returns because it can predict the time variation in volatility of equity returns.

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equilibrium relations with equities because of the default risk information that these spreads contain. An interesting result from their study is the fact that the speculative grade spread index has a superior explanatory power when compared with the investment grade one. As far as the relationship of these spreads with the Treasuries is concerned the authors find out that the spreads increase when the yields on Treasuries rise. Overall the authors conclude that IG (Investment Grade) and HY (High Yield) credit spreads have explanatory power when it comes to forecasting equity returns with high-yield being superior to investment grade spreads because of higher sensitivity to changes in perceived default risk.

2.4 Summary and Hypotheses formulation

From the theoretical framework discussed above the following conclusions can be made: - Commercial paper – Treasuries credit spread should be an useful indicator for real

economic activity and equity returns, because it contains information regarding the stance of monetary policy on a given market and the perceived by investors default risk. In this thesis although a longer-term spread is used – company credits versus government yields of the same maturities. The reason for that is the fact that at the EU market no short-term index is available and also the fact that the correlation between the short-term and longer-term indices on the US is high. Please refer to section 3 for a more detailed discussion.

- The speculative grade corporate bonds – government bonds spread should be a better indicator for equity returns as well as economic cycles because it is more sensitive when it comes to taking into account expectations for deteriorating economic conditions and increased probabilities of default.

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Therefore, the hypotheses of this study can be formulated as follows:

- H1: Credit spreads lead on equities on both markets – EU and US

- H2: High-yield credit spread is better indicator than investment grade credit spread for equity returns on both the EU and the US markets

- H3: Extremely negative excess corporate bond returns signal a turn in the cycle of equity returns

- H4: Credit spreads lead on economic growth on both the EU and the US market - H5: High-yield credit spread is better indicator for economic growth than

investment grade credit spread on both markets

Please note that in this study the excess corporate bond return is used as a proxy for credit spreads. For a detailed discussion of this choice please refer to section 3 – Data.

3. Data

In the time period selected there were two financial crises – the Internet bubble burst in 2000 and the financial crisis of 2007 – 2008. In order to test the research question and the formulated hypotheses the following data sets were obtained:

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monthly excess return over the respective government curve, monthly excess return over the LIBOR (swap) curve, the spread in bps over the government as well as swap curves, the effective duration, effective yield and yield to maturity on a monthly aggregate basis for all the bonds forming the respected indices. The credit spreads used in this study are long-term corporate bonds, both IG and HY, versus their respective Treasuries or German government bonds matched on maturities. The reason that this spread is chosen instead of the short-term one (6 months) as indicated the best by literature, is the fact that there is no short-term corporate bond index on the EU market. Also the correlation between these two spreads on the US market is high – for the IG it is 59% and for the HY index 42% so the results should be comparable. The information about these indices was extracted from the Bloomberg Terminal and the provider of the indices is Bank of America Merrill Lynch.

 As a proxy for equity returns on the different markets equity indices are used. For the EU market MSCI Europe index was chosen and for US market – S&P 500 index. Time series on monthly (S&P 500) and quarterly returns (MSCI Europe) were extracted from Datastream for the period starting January 1997 to December 2014 (215/72 observations in total). The motivation for choosing these indices lies in the fact that the companies that form the index are directly related to real economic activity on both markets.

 As a proxy for economic growth quarterly data series of total GDP value in the Eurozone and the US are used. The GDP data used for the purposes of this research is calculated based on the expenses method in the respected currency – EUR and USD. The economy growth rate is calculated by the formula: . Data set is obtained from OECD.

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analysis that the HY excess bond return should be more sensitive to economic developments, because of its nature.

For the purpose of the research the excess return over the respective government bond yield curve is used. The main motivation for not using the spread directly is that the bond indices used are dynamic which means that new bonds can leave and enter the index each month and this will in turn affect the spread, while the excess returns will not be affected by that bias. Another argument for using the excess return instead of the spread is the non-stationarity of the bps data reported by authors such as Pedrosa and Roll (1998) and Morris, Neal, and Rolph (2000). By using excess return and equity returns the non-stationarity problem is not present in our data. For stationarity tests please refer to Appendix A.

An important transformation of the data is taken in order to make the results more robust – from monthly time series quarterly data are formed. For more detailed discussion about the transformation and its necessity please refer to methodology section.

3.1 Graphical representations

In this section the development in IG, HY and equities on both markets is presented graphically and comments are given about the expected results based on the graphs.

For the EU market the relationship between the IG excess return index (EN00) and equity return (MSCI Europe) is presented in Graph 1. As it is visible from it on the IG European market there should be a relationship just as the one described above between the two variables. Also based on these observations an expectation about the time lag can be made – according to the development of both variables it is expected that the effect of IG excess bond returns on equity will be visible after 3 months.

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Graph 1: IG excess return vs equity returns EU market

Graph 2: HY excess return vs equity EU market

Graph 3 plots the development of IG versus HY excess bond return indices on the EU market. It is clearly visible that the intuitive explanation above, that HY is more sensitive to economic developments, holds in reality at the EU market. What this fact means is that the HY excess

-.08 -.04 .00 .04 .08 -.3 -.2 -.1 .0 .1 .2 .3 Q 1 199 7 Q 3 199 7 Q 1 199 8 Q 3 199 8 Q 1 199 9 Q 3 199 9 Q 1 200 0 Q 3 200 0 Q 1 200 1 Q 3 200 1 Q 1 200 2 Q 3 200 2 Q 1 200 3 Q 3 200 3 Q 1 200 4 Q 3 200 4 Q 1 200 5 Q 3 200 5 Q 1 200 6 Q 3 200 6 Q 1 200 7 Q 3 200 7 Q 1 200 8 Q 3 200 8 Q 1 200 9 Q 3 200 9 Q 1 201 0 Q 3 201 0 Q 1 201 1 Q 3 201 1 Q 1 201 2 Q 3 201 2 Q 1 201 3 Q 3 201 3 Q 1 201 4 Q 3 201 4 IG excess return Market return IG return Market return -.3 -.2 -.1 .0 .1 .2 .3 -.3 -.2 -.1 .0 .1 .2 .3 Q 1 199 8 Q 3 199 8 Q 1 199 9 Q 3 199 9 Q 1 200 0 Q 3 200 0 Q 1 200 1 Q 3 200 1 Q 1 200 2 Q 3 200 2 Q 1 200 3 Q 3 200 3 Q 1 200 4 Q 3 200 4 Q 1 200 5 Q 3 200 5 Q 1 200 6 Q 3 200 6 Q 1 200 7 Q 3 200 7 Q 1 200 8 Q 3 200 8 Q 1 200 9 Q 3 200 9 Q 1 201 0 Q 3 201 0 Q 1 201 1 Q 3 201 1 Q 1 201 2 Q 3 201 2 Q 1 201 3 Q 3 201 3 Q 1 201 4 Q 3 201 4

HY excess return Market return

Market return

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returns should be a better indicator for a change in the cycle of equity returns than IG bond index. Another interesting feature of the graph is that it seems that HY excess bond returns have steeper bottoms and higher peaks than IG excess returns which implies that HY corporate bonds should be more sensitive when it comes to measuring default probabilities. Also it seems that HY and IG excess returns move very close to one another just before a crisis occurs. For example the returns of the two classes of bonds do not differentiate that much for the period Q1 1998 – Q2 2000. After that the Internet bubble bursts and HY bond returns become more sensitive than IG, with the HY hitting a negative return of around 20% compared to only around minus 3% for the IG bonds. For the period Q1 2004 – Q1 2008 and the development after the financial crisis similar observations can be made. Overall it is clearly visible that both HY and IG bonds follow the same pattern for the data period selected.

Graph 3: HY vs IG excess bond returns EU market

Graphs 4, 5 and 6 show that similar relationships hold at the US market so the conclusions that can be reached and the expectations that can be formed remain the same. One difference is that in US excess bond returns and equity react together with no time lag. This might imply that the US market is more efficient in pricing risks and that is why equities and credits adjust simultaneously to changes in risk perception.

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Graph 4: IG excess return vs Market return US market

Graph 5: HY excess return vs Market return US market -.15 -.10 -.05 .00 .05 .10 .15 -.3 -.2 -.1 .0 .1 .2 CA 0 in de x Q 1 199 7 Q 3 199 7 Q 1 199 8 Q 3 199 8 Q 1 199 9 Q 3 199 9 Q 1 200 0 Q 3 200 0 Q 1 200 1 Q 3 200 1 Q 1 200 2 Q 3 200 2 Q 1 200 3 Q 3 200 3 Q 1 200 4 Q 3 200 4 Q 1 200 5 Q 3 200 5 Q 1 200 6 Q 3 200 6 Q 1 200 7 Q 3 200 7 Q 1 200 8 Q 3 200 8 Q 1 200 9 Q 3 200 9 Q 1 201 0 Q 3 201 0 Q 1 201 1 Q 3 201 1 Q 1 201 2 Q 3 201 2 Q 1 201 3 Q 3 201 3 Q 1 201 4 Q 3 201 4

IG excess return Market return

IG return M arket return -.3 -.2 -.1 .0 .1 .2 .3 -.3 -.2 -.1 .0 .1 .2 Q 1 199 7 Q 3 199 7 Q 1 199 8 Q 3 199 8 Q 1 199 9 Q 3 199 9 Q 1 200 0 Q 3 200 0 Q 1 200 1 Q 3 200 1 Q 1 200 2 Q 3 200 2 Q 1 200 3 Q 3 200 3 Q 1 200 4 Q 3 200 4 Q 1 200 5 Q 3 200 5 Q 1 200 6 Q 3 200 6 Q 1 200 7 Q 3 200 7 Q 1 200 8 Q 3 200 8 Q 1 200 9 Q 3 200 9 Q 1 201 0 Q 3 201 0 Q 1 201 1 Q 3 201 1 Q 1 201 2 Q 3 201 2 Q 1 201 3 Q 3 201 3 Q 1 201 4 Q 3 201 4

HY excess return Market return

HY return

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Graph 6: HY vs IG excess return US market

4. Methodology

The purpose of this section is to introduce the methods used to test the hypotheses outlined above. In order to have meaningful results some manipulations were performed on the data. Excess return over government bonds is used as a proxy for the credit spread, because as discussed by Bernanke (1990) this spread is one of the best predictors of economic development which in turn affects equity returns. Then from the monthly excess bond return series for the period January 1997 – November 2014 (215 observations) quarterly excess returns were formed. This transformation is necessary to capture trends that may not be visible on a monthly basis. The quarter excess return of bonds is formed by simply aggregating the monthly excess returns instead of using averages which may suffer from different biases. After transformation the sample contains 72 observations. The same quarterly transformation was applied to the S&P 500 index, but the MSCI Europe was already extracted on quarterly return basis from Datastream.

For testing hypotheses H1 and H2 a simple linear regression with two variables – excess corporate bond returns and equity returns will be estimated using the OLS methodology. The excess bond return variable is independent and the market return is the dependent variable.

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The variables are given the following names: - MSCI Europe is called “MARKET EU” - EN00 is called “IG EU”

- HE00 is called “HY EU”

- S&P 500 is called “MARKET US” - C0A0 is called “IG US”

- H0A0 is called “HY US”

The first step in every OLS estimation model is to plot the two variables and see whether the relationship looks linear. Graphs 7, 8, 9 and 10 show the scatter plots of the variables for the EU and US markets respectively. It is clearly visible that the relationship looks linear so the OLS estimation should provide reliable results.

Graph 7 – EU market IG scatter plot

Graph 8 – EU market HY scatter plot

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Graph 9 – US market IG scatter plot

Graph 10 – US market HY scatter plot

The main OLS equation will have the following form:

- MARKET EU/US = α + β*IG EU/US or β* HY EU/US (A)

Acknowledging the fact that credit spreads may have a reflection on equity returns with some time lag, such as the one discussed in the previous section, three lags are defined: 3-month (t-1), 6-month (t-2) and 9-month (t-3). The regression equations will take the following form:

- For 3-month lag (t-1): MARKET EU/US(t)= α + β*IG EU(t-1)/US(t-1) or β* HY EU(t-1) / US(t-1) (A1)

- For 6-month lag (t-2): MARKET EU/US(t)= α + β* IG EU(t-2)/US(t-2) or β* HY EU(t-2) / US(t-2) (A2)

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The main interest will be the β-coefficient in each regression since it will measure the sensitivity of equity returns to changes in credit spreads. Also the adjusted R2 of the regression models will be of interest since they will measure the goodness of fit of the model.

Another important aspect of the research is the test of H3 (highly negative excess bond returns will signal a turn in equity cycle returns). Therefore a distinction is made between quarters with positive and extremely negative excess bond returns on both markets. This is useful because extremely negative excess bond return will mean a sharp widening of the spread which in turn will reflect the expectations of investors for deteriorating economic conditions. These adverse conditions will affect equity returns. Table 1 below represents the minimum values of the excess return for both the EU and the US markets including the IG and HY excess bond returns and the range considered as extremely negative.

Table 1 – Extreme negative excess bond returns definition

EU market US market

IG excess return HY excess return IG excess return HY excess return

Minimum value - 5.92% - 28.82% - 10.09% - 23.65%

Maximum value 5.13% 25.83% 13.64% 23.86%

Number of

observations between minimum value and 0

24 24 27 26

Range considered in the minimum extreme

- 0.79% to - 5.92% -5.24% to -28.82% -1.20% to -10.09% - 2.84% to -23.65%

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crisis) and the maximum values are observed at the beginning of 2009 (Q1 or Q2). As it is visible, after reaching the minimum value, credits recover more gradual and steady on the EU market. A sharp contrast is the US market where the rebound of credits is much sharper and faster.

Table 2 – Development of bond returns after hitting minimum values

EU market US market

Q3 2008 Q4 2008 Q1 2009 Q2 2009 Q3 2008 Q4 2008 Q1 2009 Q2 2009

IG excess return -2.93% -5.92% 2.51% 5.13% -10.09% -6.96% 0.001% 13.64%

HY excess return -14.80% -28.82% 6.75% 25.83% -11.95% -23.65% 5.36% 23.86%

The equation with the dummy variable takes the following form:

- MARKET EU/US = α + β*DUMMYEU/US + β*DUMMYEU/US(-1) (B)

Here again the β coefficient will measure the sensitivity of equity returns to widening of the bond spread and will give the answer whether the extremely negative excess returns really can signal a change in the equity cycle.

The fourth and fifth hypotheses are tested by regressing the GDP growth on the quarterly excess bond returns for both markets – US and EU and for both grades – HY and IG. For scatter plots of the variables please refer to Appendix B. The main equation looks like that:

- GDP_growth = α + β1*IG/HY EU/US+ β2*IG/HY EU/US (-1) + β3*IG/HY EU/US (-2) (C) This equation is then tested with a RESET test for misspecification of the functional form. These tests resulted in the following adjustments that had to be made (for a more detailed discussion on diagnostic tests please refer to Appendix C):

- GDP_growth = α + β1*IGEU2+ β2*IGEU(-1)2 + β3*IGEU(-2)2 (C1) - GDP_growth = α + β1*HYEU2+ β2*HYEU(-1)2 + β3*HYEU(-2)2 (C2) - GDP_growth = α + β1*IGUS2+ β2*IGUS(-1) + β3*IGUS(-2)2 (C3) - GDP_growth = α + β1*HYUS2+ β2*HYUS(-1)2 + β3*HYUS(-2)2 (C4)

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positive at around 1.6% while both IG and HY excess returns in the same quarter are negative. Then in Q1 2008 GDP drops to around -1.7% and the IG and HY returns are again negative. This clearly shows the exponential movements that are present in the GDP data. Also another observation that can be made from the scatter plots and the data is the fact that similar positive and negative returns actually have the same impact on GDP growth. Therefore, making the dependent variables squared makes sense because of the symmetrical impact of both negative and positive excess bond returns. Similar observations can be made for the US market.

5. Results

5.1 Test of H1: Bonds lead on equities on both markets

In Table 3 the estimation results for equity returns on the EU and the US markets regressed on both IG and HY excess bond returns are presented.

On the EU market the IG bonds excess return explains about 37% (adjusted R2) of the variation of equities. The constant in the model is not significant at any level and as it turns out the IG bonds excess returns affects equities on the EU market with a 3-month time lag. The β coefficient in front of the IG EU (-1) term is 4.86 which is statistically and economically significant at 1%, 5% and 10% levels. All other coefficients in the model are not significant at any level. The coefficient suggests also that the impact on equity returns is really high. The positive sign of the coefficient means that when the investment grade bonds of non-financial institutions on the EU market earn increasing excess returns then equities will also exhibit a raise in the returns gained 3-months later. Increasing excess returns are consistent with tightening of the spread which in turn reflects improving perspective of investors for the future prospects of the economy. An explanation for this result might come from the fact that in the EU the banking sector is much larger than in the US. This means that companies on the EU market rely more heavily on bank loans when the conditions deteriorate and the capital markets are unwilling to lend more. In the US companies rely predominantly on market funding and that is why it is more likely to expect tightened lending conditions to be reflected almost immediately in equity prices. Considering this fact, a deterioration on the IG credit market in the EU might have a slower impact on companies since banks are not very fast on tightening their lending conditions to businesses.

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25

insignificant at any level except the β coefficients in front of the terms HY EU(-1), which value is 1.03 and is significant at 1%, 5% and 10% level and the HY EU(-3) which is significant at the 10% level. The sign is right and the interpretation is similar with the one discussed for IG excess corporate bond returns except for the fact that HY corporate bond returns contain information about subsequent equity returns 9-months in advance.

On the US market, it can be seen that the IG US (-1) and IG US (-2) coefficients are not significant at any level, but the IG and IG US (-3) coefficients are significant on the 1%, 5% and 10% level. This means that the IG bond returns simultaneously lead and coincide with the development in equity returns. The simultaneous movement of equities and IG bonds can be explained with the fact that the US markets are more efficient in pricing risks and therefore stocks and bonds react at the same time to changing economic conditions.

A useful insight can be generated that on the US market excess bond returns can be used as a predictor of equities 9 months in advance. This fact can be explained by taking into account that a full credit cycle lasts about 5 years, which implies that every phase of the credit cycle takes a little bit over a year. Thus when bonds start to decline because of deteriorating economic conditions, equities might still be positive. Companies then start to re-lever and use debt to pay shareholders so equities perform well. In order to confirm this explanation on the EU market, additional time lags were added to both IG and HY equation (12- and 15 months). However these time lags do not include valuable information for forecasting equities on that market. An interesting result however is the fact that the HY excess bond return on the EU market that affects equities with a 9-month lag is significant at both 5% and 10% levels in the new equation. For estimation outputs please refer to Appendix D (Tables D1 and D2).

Also the variance of excess IG corporate bond return explains about 38% of the variance of equity returns. When it comes to HY excess corporate bond returns the numbers on the US market again tell a similar story to the IG excess corporate bond returns. The HY explains about 47% of the variance of equities and all coefficients are insignificant except the ones for the HY US and HY US (-3) terms. Their signs are also positive (right) and the HY US coefficient is significant at the 1%, 5% and 10% level while the HY US (-3) is significant at only 5% and 10% level.

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26

market and over the next 9 months for the US market. Interestingly at the US market excess bond returns also have the highest impact on equity returns without any time delay, which implies superior market efficiency. This does not hold on the EU market since the impact of bonds on equities comes with a 3 month lag only (with the exception of HY being significant at the 10% level) which means that excess bond returns can give a fairly good prediction for the direction of equity returns within a reasonable time frame.

An extra regression with monthly returns instead of quarterly returns is estimated on the US market in order to see if indeed credits lead on equities with one or two months. The estimation results confirm that indeed credits (IG and HY) affect equities with a 2 – month lag. For estimation results please refer to Appendix D (Tables D3 and D4).

Table 3: IG and HY excess returns versus equity EU/US market

Note: T- statistics are presented in brackets; significance levels are presented as follows: *-significant at 10%,

**-significant at 5%, *** - **-significant at 1%

Therefore, H1 is confirmed – bond returns indeed lead on equity returns. So this insight can be used for asset allocation decisions from investors who have exposure on both markets.

InvestmentGrade High yield

Variable EU market US market Variable EU market US market

α 0.003 0.012* α 0.003 0.008 (0.312) (1.765) (0.300) (1.202) IG -0.560 1.537*** HY -0.111 0.777*** (-0.725) (6.228) (-0.721) (5.461) IG(-1) 4.866*** 0.031 HY(-1) 1.031*** -0.050 (6.178) (0.121) (8.188) (-0.355) IG(-2) 0.620 -0.049 HY(-2) -0.018 0.131 (0.787) (-0.191) (-0.113) (0.993) IG(-3) 0.885 0.693*** HY(-3) 0.211* 0.229** (1.143) (2.803) (1.694) (2.739) R-squared 0.41 0.42 R-squared 0.59 0.50

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27 5.2 Testing H2: HY is a better predictor than IG on both markets

In order to test H2, it is desirable to determine which model is better the one with HY or IG excess returns. Adjusted R2 is used in this case in order to compare models on the different markets since the dependent variable is the same – equity returns.

Looking at the EU market the adjusted R2 for the IG excess corporate bond return is around 37% which is smaller than the adjusted R2 for the HY excess corporate bond returns which is around 57%. This points out in favor of the HY regression since the differential observed is economically significant. Therefore, on the EU market H2 can be confirmed. This means that investors in the EU market should benefit when choosing the HY credit spread rather than IG credit spread as an indicator for equity returns.

At the US market the IG regression has an adjusted R2 of 38% and the HY regression has an adjusted R2 of 47%. The differential for this measure of goodness of fit is much smaller on this market. Therefore on the US market, even though both models give precise indications, the investors should choose to use the HY model.

Overall there is evidence that HY bonds better capture changing default expectations in economic downturns. Therefore, H2 can be confirmed at both markets.

5.3 Testing H3: Extremely negative excess bond returns signal a turn in equity cycle

Table 4 presents the results from equation (B). On the EU market the extremely negative excess returns of both IG and HY bonds have explanatory power as far as equities are concerned with a time lag of 3 months. This means that the large negative excess bond returns contain useful information for investors and can be used as an indicator of a change in equity return cycle. The extremely negative excess IG bond returns explain 22% of the variance in equity returns compared to 39% when HY extremely negative excess bond returns are used. This implies that investors should monitor the HY excess returns in order to identify an extremely negative return – one that is in the range described at section 4, Table 1, which will ultimately signal the change in equity return cycle.

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economic conditions companies experience difficulties in conducting their business and may even go bankrupt.

At the US market the negative excess returns of both IG and HY excess returns explain close to 27% of the variation of equity returns and both coefficients are statistically significant at the 1%, 5% and 10% level with no time lag. The economic significance however is very low and according to the data the extreme negative excess returns do not contain very useful information for investors on the US market because they cannot be used as a leading indicator. An interesting result, however, is the fact that both IG and HY regressions give the same coefficient estimates. This is the case because negative excess returns for both IG and HY bonds coincide in the time frame used.

Overall, it can be concluded that on the US market H3 can be rejected since it fails to predict the turn in the cycle of equity returns in advance, but on the EU market the extremely negative excess returns of both IG and HY bonds contain useful information for investors when it comes to predicting the turn in the cycle of equity returns 3 months in advance with the HY model being the better one. This can be explained again with the fact that the US market is more efficient when it comes to pricing risks.

Table 4: Effect of extreme negative excess returns on equities

Investment Grade High Yield

α -0.125*** -0.073*** α -0.164*** -0.073*** (3.410) (-3.359) (-5.132) (-3.359) DUMMY 0.028239 0.097*** DUMMY 0.042 0.097*** (0.906) (5.07) (1.47) (5.07) DUMMY (-1) 0.141*** 0.012 DUMMY (-1) 0.174*** 0.012 (4.52) (0.624) (6.045) (0.624) R-squared 0.25 0.29 R-squared 0.41 0.29

Adjusted R-squared 0.22 0.27 Adjusted R-squared 0.39 0.27

Note: T- statistics are presented in brackets; significance levels are presented as follows: *-significant at 10%, **-significant

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29 5.4 Testing H4: Spread leads on economic growth

Table 5 presents the results of the tests of hypotheses H4 and H5. On the EU market it is visible that the IG excess bond returns influence the GDP growth with a 3-month lag. The sign in front of the coefficient is negative and right because squared variables are used in the equation estimation. This means that when there is a positive or negative shock to the spread then GDP will contract also after 3 months.

For the HY corporate bond excess returns on the EU market, only the no lag coefficient does have a statistical and economic significance at the 10% confidence level. The coefficient is again with a negative sign, which implies similar explanation as the one provided above. But what is interesting is the fact that the HY corporate bond returns do not lead economic growth on the EU market.

On the other hand, on the US market the IG excess bond returns affect GDP growth with a 3-month lag. The coefficient is statistically significant at the 5% and 10% level. As far as the HY excess bond returns are concerned, they have a significant impact on economic growth again with a 3-month lag, but the coefficient is significant at the 1%, 5% and 10% levels. The signs are also negative and consistent with what theory would suggest. Only the sign in front of the 3-month lagged IG excess return is positive, but it is still consistent with theory since this term was not squared in the equation. (Please refer to equation C(3)).

Table 5: Effect of IG and HY excess bond returns on GDP growth

Investment Grade High Yield

α 0.01*** 0.01*** α 0.01*** 0.01*** (12.07) (13.61) (12.30) (16.99) IG -4.72*** -1.07*** HY -0.13* -0.43*** (-9.62) (-3.33) (-1.83) (-5.6) IG (-1) -6.7*** 0.06** HY (-1) -0.20 -0.25*** (-3.43) (2.30) (-1.53) (-3.58) IG (-2) 0.34 0.43 HY (-2) -0.02 0.09 (0.42) (-1.42) (-0.31) (1.23) R-squared 0.54 0.25 R-squared 0.33 0.45

Adjusted R-squared 0.52 0.21 Adjusted R-squared 0.30 0.43

Note: T- statistics are presented in brackets; significance levels are presented as follows: *-significant at 10%, **-significant

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As it is visible from Graph 11 below, the volatility of IG excess bond returns on the EU market indeed affects the GDP growth. Therefore, it cannot be concluded that a negative excess bond return will impact GDP growth since GDP reacts in a similar fashion to similar positive and negative excess returns. This means that uncertainty (high volatility) impacts GDP growth negatively with a 3-month delay on the EU market. On the US market similar observations can be made, but in addition to volatility, as it is visible from Graph 12, the negative shocks in the IG excess return have a lagged influence on GDP growth. According to Graph 13 on the HY market in the US, again the volatility of excess bond returns affects GDP growth with a 3-month lag.

Graph 11 – IG excess bond return versus GDP growth EU market

Graph 12 – IG excess bond return versus GDP growth US market -.08 -.04 .00 .04 .08 -.03 -.02 -.01 .00 .01 .02 Q 4 199 6 Q 2 199 7 Q 4 199 7 Q 2 199 8 Q 4 199 8 Q 2 199 9 Q 4 199 9 Q 2 200 0 Q 4 200 0 Q 2 200 1 Q 4 200 1 Q 2 200 2 Q 4 200 2 Q 2 200 3 Q 4 200 3 Q 2 200 4 Q 4 200 4 Q 2 200 5 Q 4 200 5 Q 2 200 6 Q 4 200 6 Q 2 200 7 Q 4 200 7 Q 2 200 8 Q 4 200 8 Q 2 200 9 Q 4 200 9 Q 2 201 0 Q 4 201 0 Q 2 201 1 Q 4 201 1 Q 2 201 2 Q 4 201 2 Q 2 201 3 Q 4 201 3 Q 2 201 4 Q 4 201 4

IG excess bond return GDP growth

IG excess return GDP growth -.15 -.10 -.05 .00 .05 .10 .15 -.03 -.02 -.01 .00 .01 .02 .03 Q 4 199 6 Q 2 199 7 Q 4 199 7 Q 2 199 8 Q 4 199 8 Q 2 199 9 Q 4 199 9 Q 2 200 0 Q 4 200 0 Q 2 200 1 Q 4 200 1 Q 2 200 2 Q 4 200 2 Q 2 200 3 Q 4 200 3 Q 2 200 4 Q 4 200 4 Q 2 200 5 Q 4 200 5 Q 2 200 6 Q 4 200 6 Q 2 200 7 Q 4 200 7 Q 2 200 8 Q 4 200 8 Q 2 200 9 Q 4 200 9 Q 2 201 0 Q 4 201 0 Q 2 201 1 Q 4 201 1 Q 2 201 2 Q 4 201 2 Q 2 201 3 Q 4 201 3 Q 2 201 4 Q 4 201 4

IG excess bond return GDP growth

IG return

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31 Graph 13 – HY excess bond return versus GDP growth US market

Overall, the conclusion that can be derived from the results is that on both markets volatility of bond returns leads on economic growth with 3 months except for the HY index on the EU market which coincides with the GDP growth, so we do not reject H4. An interesting insight is also generated that this volatility on the EU and the US bond markets has a negative impact on GDP growth. Therefore, it can be said that there is no distinction between tightening and increasing of the spread since GDP reacts negatively predominantly to the uncertainty (volatility) on both markets, with the exception at the IG US market.

5.5 Testing H5 – HY is better predictor than IG for economic growth on both markets

As far as the testing of H5 a similar approach as in section 5.1 is applied. On the European market the IG regression model explains around 52% of the variation in GDP growth rate compared to HY model which explains 30% based on adjusted R2 measure. Therefore, it can be concluded that the IG model is a better predictor for economic growth on the EU market. On the US market, however, the exact different observations can be made. The adjusted R2 equation for IG model is 21% compared to 43% for the HY model. Therefore, on the US market the HY model is better for predicting economic growth than the IG model. Caution is needed in interpreting that result since the models estimated are not exactly alike – please refer to equations C3 and C4.

-.3 -.2 -.1 .0 .1 .2 .3 -.03 -.02 -.01 .00 .01 .02 .03 Q 4 199 6 Q 2 199 7 Q 4 199 7 Q 2 199 8 Q 4 199 8 Q 2 199 9 Q 4 199 9 Q 2 200 0 Q 4 200 0 Q 2 200 1 Q 4 200 1 Q 2 200 2 Q 4 200 2 Q 2 200 3 Q 4 200 3 Q 2 200 4 Q 4 200 4 Q 2 200 5 Q 4 200 5 Q 2 200 6 Q 4 200 6 Q 2 200 7 Q 4 200 7 Q 2 200 8 Q 4 200 8 Q 2 200 9 Q 4 200 9 Q 2 201 0 Q 4 201 0 Q 2 201 1 Q 4 201 1 Q 2 201 2 Q 4 201 2 Q 2 201 3 Q 4 201 3 Q 2 201 4 Q 4 201 4

HY excess bond return GDP growth

HY return

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Overall, it is difficult to come to logical conclusions regarding H5 from the evidence presented, since, as proven in the previous section, GDP growth reacts to volatility of the spread instead of the widening of the spread. That is why it can be said that H5 cannot be rejected nor confirmed.

6. Conclusion

The results from this thesis confirm that credit spreads indeed have high predictive powers as indicated by various authors for the US market and these powers are also strong at the EU market. This research provides several useful findings that will find implication in TAA decisions that portfolio managers – both private and institutional face every day. The first important finding of the research is that credit spreads lead on equities on both markets – the EU and the US. On the EU market they lead on equities with 3-months while at the US they indicate a problem 2-months and 9-months in advance and have a significant impact on equities simultaneously with the deterioration of economic conditions which implies market efficiency with the HY model being better than IG on both markets. Second extremely negative excess bond returns, which signal a widening of the spread, do not contain useful information regarding the cycle of equity returns on the US market but both IG and HY extremely negative excess bond returns signal a turn in the equity cycle on the EU market, with HY bonds being a better predictor. Third important finding is that credit spreads indeed do forecast economic growth measured by GDP growth on both markets. What is interesting here is the fact that GDP growth reacts to the volatility in the credit spread regardless of the sign of the shock with a 3-month lag, with the IG spread being an exception on the US market (there GDP growth reacts to tightening of the spread with a 3-month lag).

7. Limitations and further research

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References:

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37 APPENDICES

Appendix A - Data stationary tests

In finance theory and practice time series data often is not stationary but stationarity is a desirable feature of the data. In the case of non stationary processes the regressions performed may be spurious and the results reached may be misleading. That is why testing the behavior of the data is of a great importance.

Therefore two tests for stationarity were conducted on the time series data – ADF (Augmented Dickey – Fuller) and KPSS (Kwiatkowski–Phillips–Schmidt–Shin). The former tests the presence of unit root in the time series by calculating a test statistic and testing the null hypothesis that there is a unit root in the data against the one sided alternative that the process is stationary. The latter tests the null hypothesis that a process is stationary around a deterministic trend against the one sided alternative that the data is not stationary. (Brooks, 2008) Results of these tests are presented in tables 2.1 for EU market data and 2.2 for US market data.

Table 1.1 – EU time series stationarity tests

ADF test:

t-Statistic Prob. MSCI Europe -6.8241 0.0000

HY Index -6.4948 0.0000

IG Index -9.16096 0.0000

Test critical values: 1% level -3.52562 5% level -2.90295 10% level -2.5889 KPSS test: LM-Stat. MSCI Europe 0.132589 HY Index 0.129801 IG Index 0.135615

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38 Table 1.2 – US time series stationarity tests

ADF test

t-Statistic Prob.* S&P 500 -6.516003 0.0000

IG Index -6.248429 0.0000

HY Index -6.951723 0.0000

Test critical values: 1% level -3.525618 5% level -2.902953 10% level -2.588902 KPSS test LM – Stat. S&P 500 0.100415 IG Index 0.079433 HY Index 0.117645

Asymptotic critical values*: 1% level 0.739 5% level 0.463 10% level 0.347

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39 Appendix B – Scatter plots

Graph B.1: IG bonds vs GDP growth EU market

Graph B.2: HY bonds vs GDP growth EU market

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40 Graph B.4: HY vs GDP growth US market

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41 Appendix C – Diagnostic tests on models

Section C.1

The purpose of this section is to describe briefly the diagnostic tests used to confirm that the models applied in this thesis are the best fit for the data. For additional and more detailed discussion please refer to Brooks (2008) textbook. This textbook is also used in the description of the diagnostic tests below. In order for OLS to present BLUE (Best Linear Unbiased Estimates) the four Gauss – Markov assumptions have to be satisfied. Below each assumption is presented and the tests for it are explained.

1. Assumption 1: Error terms in the model have zero mean (E{ut} = 0)

This assumption can only be violated when there is no constant in the model. However this is not the case in the models used so it can be confirmed that this assumption holds. If it does not R2 can be negative and any inferences made on the β coefficients can be biased.

2. Assumption 2: The variance of the error terms is constant (var {ut} = δ2)

If the error terms of the OLS regressions have a constant variance it is said that they are homoskedastic, otherwise it is said that the error terms are heteroskedastic.

This is the case when one of the explanatory variables causes the variance in the error terms not to be constant. In order to test if the assumption is violated in this sense, the most commonly used test is the White’s test. It works by obtaining the residuals (ut) from the regression and an auxiliary regression is estimated in the following form:

ut= α1 + α2x2t+ α3x3t + α4x22t + α5x22t + α1x2tx3t + vt

Then the R2 of this regression is obtained and it is multiplied by the number of observations in the sample. This follows a Chi-squared distribution and we use the Chi-squared test statistic to test the null hypothesis that the error terms are homoskedastic.

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3. Assumption 3: There is no pattern in errors (cov {ui ; uj}) = 0

When this assumption is violated it is said that there is positive/negative autocorrelation. In order to detect autocorrelation the Durbin – Watson test statistic is used. If the Durbin – Watson statistic from the estimation output is around 2 then there is no autocorrelation, when it is around 0 then there is perfect positive autocorrelation and when it is around 4 there is perfect negative autocorrelation. For a more detailed discussion about Durbin-Watson specification please refer to Brooks (2008). If this assumption is violated the standard errors of the coefficients are inappropriate and a remedy is to use the standard errors corrected with the Newey-West Heteroskedasticity and autocorrelation consistent standard errors. This is exactly the adjustment that is used in this paper if autocorrelation is detected.

4. Assumption 4: There is no correlation between the independent variables and

error terms ( cov{ut, xt} = 0)

This assumption is only violated when there are omitted variables, measurement error or reverse causality. Since it is extremely unlikely to happen in financial time series data this assumption is not tested in this paper.

5. Adopting the wrong functional form

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43 Section C.2

The purpose of this section is to present all the output from diagnostic tests made for every equation used in this thesis.

1. Testing equations A to A(3) for EU and US market equations a) Output of testing Assumption 2

Table C2.1 – White test of IG equation output EU market equation

Heteroskedasticity Test: White

F-statistic 1.188378 Prob. F(14,54) 0.3108 Obs*R-squared 16.25166 Prob. Chi-Square(14) 0.2982 Scaled explained SS 16.07405 Prob. Chi-Square(14) 0.3089

Table C2.2 – Testing for ARCH effects in IG equation on the EU market

Heteroskedasticity Test: ARCH

F-statistic 1.014575 Prob. F(5,58) 0.4175 Obs*R-squared 5.147442 Prob. Chi-Square(5) 0.3982

Table C2.3 – White test of HY equation on the EU market

Table C2.4 – White test of IG equation output US market equation

Table C2.5 – White test of HY equation output US market equation

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44 b) Testing Assumption 3 on EU and US markets

Table C2.6 – Durbin – Watson statistics output

Equation Durbin – Watson Stat Autocorrelation?

IG vs equities EU market 2.16 No

HY vs equities EU market 2.36 No

IG vs equities US market 2.02 No

HY vs equities US market 2.15 No

c) Ramsey RESET test for both EU and US markets Table C2.7 – RESET test output for IG equation EU market

Value df Probability t-statistic 0.283643 59 0.7777 F-statistic 0.080453 (1, 59) 0.7777 Likelihood ratio 0.091300 1 0.7625

Table C2.8 – RESET test output for HY equation EU market

Table C2.9 – RESET test output for IG equation US market

Table C2.10 – RESET test output for HY equation US market

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45 2. Testing equation B

a) Testing Assumption 2

Table C2.11 – White’s test for Dummy IG on EU market

Table C2.12 – White’s test for Dummy HY on EU market

Table C2.13 – White’s test for Dummy IG/HY on US market

b) Testing Assumption 3

Table C2.14 – Durbin – Watson statistics for dummy equations

Equation Durbin – Watson Stat Autocorrelation?

IG dummy vs equities EU market 2.36 No

HY dummy vs equities EU market 2.45 No

IG dummy vs equities US market 1.92 No

HY dummy vs equities US market 1.92 No

c) Ramsey RESET test for both EU and US markets Table C2.15 – RESET test for IG Dummy equation EU market

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46 Table C2.16 – RESET test for HY Dummy equation EU market

Table C2.17 – RESET test for IG/HY Dummy equation US market

Value df Probability t-statistic 0.141166 67 0.8882 F-statistic 0.019928 (1, 67) 0.8882 Likelihood ratio 0.021114 1 0.8845 3. Testing equation C1 to C4 a) Testing Assumption 2

Table C2.18 – White’s test for IG equation on EU market

Table C2.19 – White’s test for HY equation on EU market

Table C2.20 – White’s test for IG equation on US market

economic growth on the EU and the US markets” “Relationship between credit spreads, equities and Master Thesis

Master Thesis

“Relationship between credit spreads, equities and