Are the High-yield Bond and Stock Markets Really Similar? Evidence from. Interactions with the Energy Markets

Transcription

1 Are the High-yield Bond and Stock Markets Really Similar? Evidence from Interactions with the Energy Markets Alper Gormus, Ugur Soytas and Saban Nazlioglu Abstract High-yield bonds hold a particularly unique space in the debt market. From many aspects, literature suggests these assets to behave more like stocks than bonds. Given the significant similarities between the high-yield bond and stock markets, it is expected for these markets to be similarly affected by certain outside factors. Some shocks, including the ones from energy markets, are known to impact the entire stock market and not just related company shares. Since high-yield bond portfolios include some amount of energy company debt, the recent volatility in energy prices has been particularly concerning to market participants. However, the question of whether these shocks only impact energy company bonds or the entire high-yield bond market - as they do with the stock market - still remains unanswered. This study attempts to address that question by exploring the dynamic relationships between the high-yield bond and energy markets. Price transmission tests, which account for gradual structural shifts, suggest oil and ethanol markets significantly impacting the high-yield bond market. Furthermore, volatility tests find uni-directional volatility transmitting from energy markets to the high-yield bond market. Keywords: high-yield bonds, gradual structural shifts, volatility transmission, energy markets JEL Classification: G1; C32; C58.

2 I. Introduction Literature suggests high-yield bonds to behave more like stocks than bonds (Hong et al. 2012; Downing et al. 2009; Zhang and Wu, 2014; Blume et al. 1991, and others). From the stock market s perspective, outside shocks related to a company s business model is expected to drive those share prices. However, some the same shocks are also found to impact the entire stock market. Similarities between the stock market and the high-yield bond market could warrant them to give similar reactions to certain outside shocks. The recent fluctuations in energy markets have created an interesting environment for the participants of all market types. While the implications of these price shocks are widely discussed, there has been a particular emphasis on their significance for the high-yield bonds. High-yield bond portfolios are known to hold a varying amount of U.S. energy company debt. With the downward spiral of the oil market, energy companies started decreasing their near-term outlooks and, in return, this pushed investors to further decrease their exposure to associated assets. In addition to energy companies, numerous studies have shown energy markets to be influential on the entire financial market structure (Sim and Zhou, 2015; Zhang et al. 2015; Kang et al. 2015; Nazlioglu et al. 2013; Arouri and Nguyen 2010; Sari et al. 2010; Driesprong et al and others). While a change in energy prices is expected to impact energy company bonds, the significance of these fluctuations on the overall high-yield bond market needs to be further investigated. If the energy prices are found to impact the high-yield bond market as a whole and not just the energy company bonds, this could have significant implications for the debt-policy and the optimal leverage structure decisions of all companies 2

3 participating in that market. Furthermore, investors and speculators would significantly benefit from such information when making portfolio and hedging decisions. In order to investigate whether the high-yield bond market responds similarly to energy price shocks, we test the price-level and volatility transmission relationships between the high-yield bond market and energy markets. In addition, we introduce a simple econometric modification which takes gradual structural shifts into consideration. Our modified model augments a well-recognized price transmission framework with a Fourier approximation and has significant advantages over the cointegration, VEC, ARDL and several other models frequently used in literature. According to our simulations, this approach is more robust and should be preferred for larger sample sizes. In particular, the oversizing problem accompanying the conventional approaches is significantly decreased when such shifts are taken into consideration. The empirical findings show prices from the oil and ethanol markets transmitting to the high-yield bond market. As for the volatility shocks, we find the volatility of all energy markets we tested transmitting to the high-yield bond market. The remainder of this paper is organized as follows: Section II presents the literature review. Section III describes the development and viability of empirical methods. Section IV reports and discusses the empirical results. Section V concludes the paper. 3

4 II. Literature Review There is a large body of research which evaluate the structure, behavior, and pricing of corporate bonds (Aboody et al. 2014; Bansal et al. 2014; Chen et al. 2013; Bao et al. 2011; May 2010 and others). Aside from representing a large portion of the overall debt market, the corporate bond market is found to be comparatively less liquid and informationally less efficient (Bittlingmayer and Moser; 2014). Although the entire bond market can present some uniform characteristics, there are significant differences between investment and noninvestment grade bonds (Barnhill et al. 2000). High-yield bonds occupy a large portion of the corporate bond market. In 2012, the yearly issuance of high-yield bonds reached $346 billion according to Forbes. One of the significant differences between high-yield bonds and investment grade bonds is that high-yield bonds behave like both bonds and stocks (Blume et al. 1991). Analyzing the specific bond characteristics, Hong et al. (2012) found that high- yield bond returns can be predicted using the historical stock market returns. On a similar note, Downing et al. (2009) demonstrated that the stock market predicts nonconvertible bonds rated BBB or lower. However, they indicated the same prediction cannot be made for safer bonds. Furthermore, Zhang and Wu (2014) showed that the stock market and the high-yield bond market are intimately related to each other; especially during bear market periods. In addition, they found that VAR based models are better at predicting high-yield bond returns compared to AR models or naïve estimation. Given that high-yield bonds are closely related to stocks, one could expect those bonds to be similarly sensitive to shocks that impact the stock market energy price shocks in particular. 4

5 Energy markets, especially the oil market, are shown to significantly influence equity markets, currency markets and the commodity markets in general (Zhang et al. 2015; Nazlioglu et al. 2013; Kang et al. 2015; Sari et al and others). As econometric models improve and the markets experience new shocks, the direction of these relationships are found to differ in literature. Some studies suggest oil prices to have a positive relationship with stock market returns in the short-run and the interaction to reverse in the long-run (for example: Miller and Ratti 2009). However, other studies such as the one by Sim and Zhou (2015) suggest large negative oil price shocks to have a positive impact on the stock market especially in bull markets. Furthermore, in their 2017 study, Mensi et al. found strong evidence of tail dependence between oil prices and major developed stock markets (S&P500, stoxx600, DJPI and TSX indexes) they tested. In addition to oil prices, other alternatives such as natural gas are also shown to be significant for the equity markets. As expected, direct dependence from related industries in the stock markets to energy markets, such as natural gas and oil, is found to fundamentally drive the performance of those companies (Ordu and Soytas, 2015). While these asset groups can behave similarly in certain situations, it might not be the case in others. As evidence, Aloui et al. (2014) tested the relationship between oil and natural gas prices from a portfolio risk management perspective and found an asymmetric transmission between the two markets. Oil and natural gas markets are observed to move together during bullish periods and differ significantly during bearish periods. Our study includes oil, natural gas and also adds ethanol as an additional alternative to oil. 5

6 Aside from price transmission, energy market volatility also plays a significant role in the behavior of equity markets. Diebold and Yilmaz (2012) comprehensively examined the stock, bond, foreign exchange, and commodity market volatility transmissions. They showed that following the recent global financial crisis, volatility transmission between the assets has increased. In 2013, Mensi et al. evaluated the volatility transmission between several markets including the U.S. stock market. Their VAR-GARCH model not only showed a significant volatility relationship between the U.S. stock market and oil prices, but also suggested the interaction to be the strongest among all other markets they tested. In addition, Mollick and Assefa (2013) showed that, while there was a significant impact of oil price volatility on the U.S. stock market, the interaction varied over time. More recently, further evidence has been provided for the volatility interactions. In 2015, Du and He demonstrated the volatility transmission between the stock market and oil prices to be strong; however they also found the bidirectional transmission to be stronger after the 2008 financial crisis. Similarly, Le and Chang (2015) showed the oil volatility impacts to be significant, but varying depending on the market type, location and time periods evaluated. Although the close relationship between stocks and high-yield bonds could warrant energy price shocks to be equally important for both asset groups, the overall bond market has also been shown to react to energy market shocks. Kang et al. (2014) found that a positive oil demand shock decreases the aggregate U.S. Bond Index returns. When evaluated using a two-year horizon, they found that structural shocks in the oil market help explain about 25% of the variation in bond index they used. From purely an 6

7 investment bond perspective, Wan and Kao (2015) found that positive shocks in oil prices decrease the spreads between the AAA and BAA rated bonds. Due to the characteristic similarities between the high-yield bond market and the stock market and the stock market s sensitivity to energy market shocks, we see value in analyzing the impact of those shocks on the overall high-yield bond market. While we evaluate these interactions from price and volatility transmission perspectives, our simple modification to the conventional price-transmission model accounts for gradual structural shifts. This approach has significant advantages over the traditional cointegration and Vector Error Correction (VEC) procedures such as the Johansen- Juselius (JJ) approach (Johansen 1988, 1991; Johansen and Juselius, 1990), Autoregressive Distributed Lag Models (ARDL) (Pesaran and Shin, 1999; Pesaran et al. 2001) and the conventional Toda and Yamamoto (TY) (1995) procedure. III. Testing procedures III. A Price transmission methodology The concept of price transmission is essentially testing to see whether the historical price information in one variable have predictive power in another. Traditional transmission tests have been heavily criticized in the literature due to spurious regression problems based on non-stationarity of the variables and non-robust results when there are structural breaks. As a response, cointegration based models have been developed to overcome both of these problems. While most of the proposed models that rely on cointegration testing and estimation are not applicable in the face of arbitrary integration orders (such as the VECM procedures), other models (including the ARDL models) have the risk of carrying the estimation biases of the cointegrating 7

8 equation back into the analysis via the error-correction term. The conventional TY price transmission procedure doesn t suffer from those problems and has been popular in literature. Although the TY procedure eliminates the need for cointegration tests and estimation, it does not have a structural-shift component. In addition, any workaround to the model requires structural shifts to be abrupt and arbitrarily guessed beforehand. The simple modification we propose here addresses both problems. It does not suffer from risks related to testing for cointegration relationships and the Fourier extension allows for the existence of structural shifts - including the gradual ones which are harder to identify. The conventional price transmission tests employ a Vector Autoregression (VAR) framework. In these approaches, however, structural shifts create a significant problem. Monte Carlo simulations by Ventosa-Santaularia and Vera-Valdés (2008) show that when data generating process has structural shifts, the null of no-transmission can be rejected even though the two variables do not have any transmission between them. Enders and Jones (2015) find similar results using Monte Carlo simulations which indicate ignoring structural breaks in VAR models result in a misspecification error. This, in-turn, leads transmission tests to be biased towards falsely rejecting the null hypothesis. In other words, inferences from a standard transmission analysis may be misleading when structural breaks are ignored or improperly taken into account. These findings not only indicate the importance of accounting for any structural shifts but also necessitate a careful treatment of how breaks are captured. The traditional approach to capture structural shifts is to use dummy variables in which shifts are assumed to occur instantaneously (for example, Perron, 1989; Zivot and Adrews, 1992; Lee and Strazicich, 2013, Gregory and Hansen, 1996). In addition to the 8

9 dummy variable approach, and due to structural changes in time-series typically being gradual in nature, tests based on a gradual transition approach were proposed (inter alia, Leybourne at al., 1998; Kapetanios et al., 2003). For these methods, there is still a need to know the dates, number and the functional forms of the breaks. To deal with these problems, Becker et al. (2006), Enders and Lee (2012a, 2012b) and Rodrigues and Taylor (2012) developed the unit root tests with a Fourier approximation which is based on a variant of Flexible Fourier Form by Gallant (1981). The Fourier approximation captures the dynamics of series with structural break(s) by using a small number of lowfrequency components. This approach also does not require prior knowledge of the number and/or dates of the breaks. In a VAR specification, controlling for structural breaks and determining the original source of breaks is difficult because a break in one variable potentially causes shifts in other variables (Ng and Vogelsang, 2002; Enders and Jones, 2015). Enders and Jones (2015) in a recent paper employed a Fourier approximation by using small number of low frequency components in order to simplify determination of the form of shifts and estimation of the number and dates of breaks in a VAR framework. They showed that the standard price transmission test has reasonable size and power properties when the breaks are sharp and performs much better when the breaks are gradual. The standard price transmission analysis is sensitive to the unit root and cointegration properties of the VAR model. Therefore, it necessitates testing for unit root and co-integration for transmission inferences. This is due to the Wald test not only having a non-standard distribution if the variables in VAR model are integrated or cointegrated, but also depending on nuisance parameters (Toda and Yamamoto, 1995; 9

10 Dolado and Lütkepohl, 1996). The TY approach overcomes these problems and is robust to unit root and co-integration properties of the VAR system. The TY method is estimated using the VAR (p+d) model where p is the lag lengths and d is the maximum integration order of variables 1. The lag-augmented VAR approach is based on estimating a VAR model in level-form of variables, and does not necessitate any pre-testing. By extending the TY framework for gradual structural shifts using a Fourier approximation, we propose a novel and simple approach that overcomes most of the problems identified so far. III. B Modifying the Conventional Model In order to account for structural shifts in the TY price transmission framework, we relax the assumption of the constant nature of the intercept terms ( ) over time and define the VAR (p+d) model as: y t = α(t) + β 1 y t β p+d y t (p+d) + ε t (2) where the intercept terms (t) are the functions of time and denote any structural shifts in y t. In order to capture structural shifts as a gradual process with an unknown date, number and form of breaks, the Fourier approximation is defined by: n α(t) α 0 + γ 1k sin ( 2πkt T ) + γ 2k cos ( 2πkt T ) k=1 n k=1 (3) where n is the number of frequencies, 1k and 2k measures the amplitude and displacement of the frequency, respectively. By substituting equation (3) in equation (2), we obtain 1 It is clear that both methods will yield the same statistic when d is equal to 1. 10

11 n y t = α 0 + γ 1k sin ( 2πkt T ) + γ 2k cos ( 2πkt T ) + β 1 y t β p+d y t (p+d) + ε t (4) k=1 n k=1 On a side note, large value of n is most likely to be associated with stochastic parameter variation, decreased degrees of freedom and also can lead to the over-fitting problem. A single Fourier frequency on the other hand mimics a variety of breaks in deterministic components regardless of date, number, and form of breaks (Becker et al., 2006). Therefore, we can use a single frequency component and define (t) as α(t) α 0 + γ 1 sin ( 2πkt T ) + γ 2cos ( 2πkt T ) (5) where k denotes the frequency for the approximation. By substituting equation (5) in equation (2), we obtain y t = α 0 + γ 1 sin ( 2πkt T (6) ) + γ 2cos ( 2πkt T ) + β 1y t β p+d y t (p+d) + ε t In this specification, testing the null hypothesis of no-transmission is the same as it is in equation (1) and the hypothesis can be tested using Wald statistic which has the asymptotic chi-square distribution with p degrees of freedom. Our TY transmission analysis with the Fourier approximation requires determining the optimal number of frequency (k) and lag lengths (p). A common approach in determining p is to utilize an information criterion such as Akaike or Schwarz. This approach also can be used for equation (5) with a slight modification since it also requires the determination of frequency k. (Enders and Holt, 2012). Specifically, we estimate the VAR models with combinations of k and p in which they go 11

12 to (the maximum number of Fourier frequency) and (the maximum number of number of lags). We then select the optimal number of k and p using the smallest value provided by the information criterion. In that respect, we determine the optimal k and p using the Akaike information criterion and then apply the transmission restriction as it is in the TY approach. This model is now able to accommodate structural shifts in any form and number in addition to advantages of TY approach. III.C Size and power analysis for the modified price transmission tests In order to investigate the size and power properties of the TY approach with a Fourier approximation (here after Fourier TY) and to compare to those of the conventional TY procedure, we consider a simple VAR (1) model which is described as: y 1t = d 1t + α 11 y 1t 1 + α 12 y 2t 1 + ε 1t (7) y 2t = d 2t + α 21 y 1t 1 + α 22 y 2t 1 + ε 2t (8) where d 1t and d 2t contain structural shifts and ε 1t and ε 2t are i.i.d. (independently and identically distributed) random variables. We describe four different structural shift types in y 1t and one sharp shift in y 2t which are same to those in Enders and Jones (2015). More specifically, the shift types are as follows: Temporary break: d 1t = 0 if 0.45T < t 0.75T, else d 1t = 3 Change in slope: d 1t = t/w if t < T/2, else d 2t = t/w LSTAR break: d 1t = 3/[1 + e (0.05/w)(t 2T/3) ] ESTAR break: d 1t = 3[1 e ( (1/w2 )(t 2T/3)^2 ] Sharp break: d 2t = 3 if t < T/3 and 0 otherwise 12

13 where the parameter w = T/2T so that the breaks do not vanish as the sample size T increases (see, Enders and Jones, 2015). The above description allows the generated y 1t to include one of gradual break types and y 2t to include one sharp break. Regardless of how the breaks are generated, we use a Fourier approximation to see how the approximation is able capture the essentials of structural shifts. We define two different parameter sets which are A 1 = [ ] and A 2 = [ ]. Accordingly, y 1t and y 2t are both I(1) and hence the maximum integration order of variables d is one. The parameter set in A 1 (A 2 ) allows us to evaluate the size (power) analysis. The recent works in the price transmission literature have relied on bootstrapping critical values. This approach helps to increase the power of test statistic in small samples as well as being robust in the unit root and co-integration properties (see Mantolos, 2000; Hatemi-J, 2002; Hacker and Hatemi-J, 2006; Balcilar et al., 2010). In order to compare the small sample properties of the asymptotic chi-square distribution with those of the bootstrap distribution, we employ the residual sampling bootstrap approach originally proposed by Efron (1979). Below, we briefly describe the bootstrap procedure for the Fourier TY test. In the first step, equation (2) is estimated under the null hypothesis of no-transmission. Then, the bootstrap sample y t is generated as: y t = α (t) + β 1y t β p+d y t (p+d) + ε t (9) where t=1,,t, the parameters represent the estimated coefficients in the first step, and ε t are i.i.d. observations drawn from the empirical distribution (F ε). This puts weight 1/T to the centered residuals (ε t ε ). The bootstrapping approach is based on drawing a 13

14 number of bootstrap samples from the restricted model. We estimate this model under the null hypothesis via calculating the bootstrap test statistic by repeating it Nb times. The (1 α) th quantile from the resulting set of bootstrapped distribution is the bootstrap critical value for the α level of significance. The null hypothesis is then rejected if the Wald statistic exceeds the bootstrap critical value. The simulations are replicated 1,000 times and the size and power of the TY and Fourier TY tests are conducted for 10 percent level of significance. Note that while the TY test ignores the structural shift and only includes intercept as a deterministic term, the Fourier TY test captures the structural shifts by means of a Fourier approximation. In the Fourier TY test, we first estimate equation (6) which uses a single frequency and then estimate equation (5) which uses cumulative frequencies. This way, we can evaluate whether using either single frequency or multiple frequencies matter for the small sample performance. The simulation results are reported for both the asymptotic chi-square distribution and the bootstrap distribution with 1,000 replications. Note that since the 10 percent bootstrap critical value would change in each Monte Carlo simulation, we compare the Wald statistic with the bootstrap critical value in each replication. In order to compare the small sample performance of the asymptotic and bootstrap distributions, we consider different sample sizes (T=20, 50, and 100). We first focus on the size of the tests. The simulation results in Table 1 provide interesting and insightful findings. When sample size is small (T=20), the desirable size properties are obtained by the Fourier TY test with k=3. In other words, it is possible to say that the TY test is likely to outperform the Fourier TY test in small samples due to cumulative frequencies leading to size distortions. The bootstrap distribution seems to show more desirable small sample properties. However, as the sample size grows, the 14

15 importance of taking structural shifts into account becomes apparent. Furthermore, the difference between asymptotic and bootstrap distributions disappears. If the sample is increased to 50 observations, while the TY test appears to keep its good size properties with the exception in the slope shifts, the Fourier TY test has slightly improved power. In different frequencies, the Fourier TY test provides the desirable size properties even with a slope break where the TY test seems to be oversized. As the number of observations continues to grow, the importance of considering the structural shifts in the price transmission analysis becomes obvious. When the sample size T=100, the TY tests have severe size distortion problems, but the TY test with Fourier approximation seems to minimize the size distortions. In particular, the Fourier TY test with three cumulative frequencies (n=3) appears to have good size properties. Table 1: Simulation results for size analysis TY Fourier TY Single frequency Cumulative frequencies k=1 k=2 k=3 k=1,2 k=1,2,3 Shift χ 2 B χ 2 B χ 2 B χ 2 B χ 2 B χ 2 B T=20 S S2 S S T=50 S S S S T=100 S S S S Notes: The size properties of the TY approach with Fourier approximation are reported in the table.χ 2 is the asymptotic distribution and B is the bootstrap distribution with 1,000 replications. Size is based on the parameter set A 1. The number of Monte Carlo replications is 1,000. k denotes the frequency for the approximation and T 15

16 represents the sample size. The size probabilities are based on the 10 percent level of significance. S 1 is temporary break, S 2 is slope break, S 3 is LSTAR break, and S 4 is ESTAR break. Single frequency is based on equation (6); cumulative frequencies are based on equation (5). Size distortions are more apparent in small samples. Bootstrap distribution also fares better in small samples. In the face of a gradual slope shift, the Fourier TY has better size properties than the conventional TY. The simulation results for the power of the test are reported in Table 2. The power analysis shows that as the number of observations increase, the power of both the TY and the Fourier TY tests increase as well. More specifically, even though the tests do not have high power when T=20, the power quickly reaches to one when the number of observations increases to 50. Last but not least, using either the asymptotic or bootstrap distribution does not matter for the power of the test when the sample size grows. Table 2: Simulation results for power analysis TY Fourier TY Single frequency Cumulative frequencies k=1 k=2 k=3 k=1,2 k=1,2,3 Shift χ 2 B χ 2 B χ 2 B χ 2 B χ 2 B χ 2 B T=20 S S S S T=50 S S S S T=100 S S S S Notes: The power properties of the TY approach with Fourier approximation are reported in the table. χ 2 is the asymptotic distribution and B is the bootstrap distribution with 1,000 replications. Power is based on the parameter set A 2. The number of Monte Carlo replications is 1,000. k denotes the frequency for the approximation and T represents the sample size. The power probabilities are based on the 10 percent level of significance. S 1 is temporary break, S 2 is slope break, S 3 is LSTAR break, and S 4 is ESTAR break. Single frequency is based on equation (6); cumulative frequencies is based on equation (5). Power increases quickly with sample size. Asymptotic and bootstrap results also converge rapidly with sample size. Fourier TY has desirable power properties in large samples. 16

17 To sum up for practitioners; as the number of observations increase and the null hypothesis of no-transmission is rejected with the TY test but not the Fourier TY test, it is recommended to interpret the findings based on the Fourier TY test only. In particular, the Fourier TY test with a single frequency is preferable with a sample size of around 50 while the Fourier TY test with cumulative frequencies is more reliable when the sample size is around or larger than 100. If one works on small sample sizes (for instance T is around 20 observations), the TY test seems to have less distortions in the results. This finding can be viewed as evidence of effects of structural shifts being manifested in longer time horizons. If both the TY and the Fourier TY test reject the null hypothesis of no-transmission, this result would provide a robust conclusion of price transmission. Last but not least, while we recommend the use of bootstrap distribution in small samples, there is no need to bear the computational burden of bootstrapping distribution as the sample grows. III. D Volatility transmission methodology In addition to price transmission methods as previously described, this study also employs a Lagrange multiplier (LM) based volatility transmission test developed by Hafner and Herwartz (2006). We utilize this approach in order to assess the existence and direction of dynamic volatility transmission between the high-yield bonds and energy prices. Some of the more common volatility transmission tests (Cheung and Ng, 1996; Hong, 2001) utilize univariate GARCH 2 models and cross-correlation functions of 2 Since the focus of this paper is to investigate volatility transmission using the causality-in-variance approach, we do not outline the details of ARCH and GARCH models in order to save space. Please refer to Engle (1982), Bollerslev (1986), and Bollerslev et al. (1992) for a detailed explanations of the volatility models. 17

18 the standard residuals. This approach suffers from significant oversizing effects especially when the volatility processes are leptokurtic and require a selection of lead and lag orders (Hafner and Herwartz, 2006). To combat this issue, Hafner and Herwartz (2006) developed the LM based volatility transmission approach which does not suffer from those issues. In addition, their method has an increasing power as the sample size grows. Hafner and Herwartz (2006) define the initial model as follows: (10) where and are respectively the standardized residuals and the conditional variance (volatility) for the series i. and are the squared disturbance term and the conditional variance for the series j respectively. The null hypothesis for notransmission is and is the alternative hypothesis which implies that transmission exists. The log-likelihood function of (Gaussian) is used to achieve where are the derivatives of the likelihood function within GARCH parameters. The LM for the volatility transmission is: (11) where. 18

19 has asymptotic chi-square distribution with two degrees of freedom. IV. Empirical Analysis IV. A Data analysis Our study employs four time-series variables: S&P U.S Issued High-Yield Bond Index (Ticker: SPUSCHY; we refer to this variable as HYBX in our study) and the futures prices for oil, natural gas and ethanol obtained from the WRDS database. Due to the relatively new inception date of the bond index, our data is restricted to daily observations from May 17, 2005 to June 22, According to Standard and Poor s, SPUSCHY index tracks the performance of U.S. dollar denominated and belowinvestment-grade corporate debt publicly issued in the U.S. markets by U.S.-based companies. Although the sample size is about ten years, the time-frame includes the recent global financial crisis as well as several large energy market fluctuations; hence, accounting for structural shifts is necessary. Before drawing inferences from the price transmission and the volatility analyses, we analyze the properties of the data. Figure 1 plots the dynamics of energy prices and the high-yield bond index (HYBX). Even though it is difficult to observe a clear relationship between the oil prices and HYBX over the complete dataset, we see a comovement between them from approximately 2008 to While the oil prices seem to fluctuate in a narrow band for the period, HYBX has an increasing trend. In addition, HYBX continues to increase even when oil experiences a sharp decline in mid These changing relationships signal the possible existence of structural shifts. Figure 1: The dynamics of high yield bond index and energy prices 19

20 120 HYBX Oil HYBX NatGas HYBX Ethanol For a closer investigation of the data characteristics, we look at Table 3 in which the descriptive statistics are summarized. All of the variables except ethanol have a wide range of fluctuations evidenced by the higher differences between minimum and maximum values. While the ethanol and natural gas prices present smaller standard 20

21 deviations with respect to the oil prices, the HYBX has the highest standard deviation. An interesting data characteristic is presented by the coefficient of variation (ratio of standard deviation to mean) which is considered to be a simple measure of volatility. We see oil and ethanol prices having similar volatility structures while natural gas prices are significantly more volatile. The coefficient of variation comparison between oil prices and HYBX show them to be very similar; possibly signaling a similar volatility structure. Our LM-GARCH based volatility measure, which we calculate later in this study, present a much more reliable analysis of this concept. Regarding the asymmetry and distribution characteristics of the data, we observe all of the series to have positive skewness and hence right tailed. The kurtosis statistics signal to non-normal distribution which is also supported by the Jarque-Bera statistic that rejects the null hypothesis of normality. Table 3: Descriptive statistics HYBX Oil Natural Gas Ethanol Mean Maximum Minimum Standard deviation Coef. of variation Skewness Kurtosis Jarque-Bera Observations Notes: First and second moments are given by the mean and standard deviation. Second and third moments are listed as skewness and kurtosis. None of the prices appear to be skewed, but there is evidence of leptokurtic shape for natural gas and ethanol. Jarque-Bera refers to the normality test statistics. It is significant at the 1% level for all prices indicating non-normality. According to the standardized spread measured by coefficient of variation, natural gas prices take the lead followed by the high-yield bond index. *** indicates statistical significance at %1 level. Table 4 represents the correlation coefficients between the variables and we observe some interesting linear relationships. Although we would have expected higher 21

22 correlations between HYBX with the oil prices than those with natural gas and ethanol, the results indicate otherwise. The highest correlation is observed to be between natural gas and HYBX where the relationship is negative (also seen in Figure 1 beginning in 2009). These statistics related to degree of transmission could be severely miscalculated if there are structural breaks in the dataset. Since we do suspect structural shifts, the correlation coefficients in table 4 should be interpreted with caution 3. Table 4: Correlation matrix HYBX Oil Natural Gas Ethanol HYBX 1.000*** Oil 0.393*** 1.000*** Natural Gas *** *** 1.000*** Ethanol 0.051** 0.478*** 0.158*** 1.000*** Notes: The pairwise correlation coefficients are reported in the table. *** and ** indicate statistical significance at 1 and 5 percent levels, respectively. All bi-variate correlation coefficients are significant. HYBX has significant correlations with energy prices at varying magnitudes as well as with different signs. This indicates the need for further study of the link between HYBX and different energy prices. We finally examine the nature of shocks to the series and employ a battery of conventional unit root tests: ADF test of Dickey and Fuller (1979), DF-GLS test of Elliot et al. (1996), and KPSS test by Kwiatkowski et al. (1992). While the ADF and DF-GLS methods test for the null hypothesis of the existence of a unit root, the KPSS test has stationarity as the null hypothesis. These conventional unit root tests, however, do not take structural shifts into consideration. In order to account for structural breaks in the unit root analysis, we conduct two separate unit root tests. The first test developed by Lee and Strazicich (2013) is based on the Lagrange Multiplier statistic with one 3 It is important to note that correlation measures linear dependence and does not indicate the existence or the direction of price transmission. The concept of transmission implies a predictive power from one price variable to the other. It is, therefore, required to employ advanced econometric tools in determining the transmission between high-yield bonds and energy prices. 22

23 structural break 4. The second test developed by Enders and Lee (2012b) is based on the conventional ADF regression which is augmented with the Fourier approximation 5. The results of the unit root tests are reported in Table 5. The HYBX, oil prices and natural gas prices are found to have unit root behavior according to all of the tests we employed. The ethanol prices seem to be stationary according to the ADF and KPSS tests, but not stationary according to the DF-GLS statistic. The results from the unit root test with a sudden structural shift proposed by Lee and Strazicich (2013) show that the null hypothesis of unit root cannot be rejected for all of the variables. The break date the end of October in the oil prices matches with the start of the oil price hike in The break dates for the natural gas and ethanol prices correspond to the oil price slump in 2008 while the break date for the HYBX coincides with the beginning of its upward trend in Finally, the results from the unit root test with gradual structural shifts by Enders and Lee (2012b) indicate the null hypothesis of unit root cannot be rejected for any of the variables. Hence, from the unit root perspective, modeling structural shifts as sudden or gradual does not seem to affect the behavior of the series. As a summary, the unit root analysis supports the evidence on the nonstationary behavior of the series and implies the existence of permanent shocks. 4 Even though our dataset includes 2541 observations, due to the relatively short time-span (10 years), we opted to employ the structural shift test with one break. 5 In order to save space, we omit the details of unit root tests. An interested reader is referred to the cited papers. 23

24 Table 5: Results from unit root tests Panel A: No shift HYBX Oil Natural Gas Ethanol ADF *** DF-GLS KPSS 5.925*** 1.124*** 3.784*** Panel B: Structural shift LM Break date Fourier ADF Frequency Notes: LM: Lee and Strazicich (2013) LM unit root test with a break. Fourier ADF: Enders and Lee (2012b) ADF unit root test with Fourier approximation. Unit root tests with no shift include a constant term. Unit root tests with shift include a structural shift in the constant term. The optimal lag(s) were determined by Schwarz information criterion for augmented Dickey-Fuller (ADF), Dickey-Fuller GLS de-trended (DF-GLS), and Lagrange Multiplier (LM) tests by setting maximum number of lags to 12. The optimal frequency and lags were determined by Schwarz information criterion for Fourier ADF by setting maximum number of lags to 12 and of Fourier frequency to 3. Bartlett kernel method for spectral estimation and Newey-West method for bandwidth were used for the KPSS test. ADF critical values are (1%), (5%), (10%), DF-GLS critical values are (1%), (5%), (10%), KPSS critical values are (1%), (5%), (10%), LM critical values are (1%), (5%), (10%). See Enders and Lee (2012b: 197) for the critical values for Fourier ADF. *** indicates statistical significance at 1 percent. IV. B Price transmission analysis The results of the traditional TY test are reported in Table 6. The null hypothesis no-transmission from oil prices to the HYBX and from HYBX to oil prices is rejected. This indicates that the price transmission analysis, which ignores any type of structural shifts, provide evidence of a feedback information flow between oil prices and HYBX. The null hypothesis of no-transmission between natural gas prices and HYBX cannot be rejected in favor of any direction. In other words, the results do not provide any evidence of information flow from natural gas prices to HYBX or vice versa. An interesting finding is that the null is rejected from ethanol prices to HYBX at a 1 percent level of significance. This result suggests the dynamics of ethanol prices providing at least some information in predicting the behavior of HYBX. 24

25 Table 6: Results from Toda-Yamamoto price transmission test HYBX Energy Prices Energy prices HYBX p Wald χ 2 -pval B-pval Wald χ 2 -pval B-pval Oil *** *** N. Gas Ethanol *** Notes: Toda and Yamamoto (1995) price transmission test statistics are reported in the table. > denotes the null hypothesis of no-transmission. Maximum p are respectively set to 12, then optimal p is determined by Akaike information criterion. χ 2 -pval denote the chi-square p-values of the Wald test statistics. Bootstrap p-values (B-pval) are based on 1,000 replications. TY test is based on equation (1). *** indicates statistical significance at 1 percent. While the conventional price transmission analysis, which does not account for structural breaks, supports the significance of energy markets on the HYBX, it also shows a transmission from HYBX to oil prices. This is an unexpected result. As it is discussed earlier and shown by the simulation analysis, the traditional transmission approach tends to over-reject the null of no-transmission if the structural breaks in the series are ignored. In order to combat this problem we augment the model with a Fourier approximation. As our simulations suggest, the Fourier-augmented model is more robust. This is particularly true as the number of observations increase. To utilize this new approach, we first employ a single frequency in the testing procedure and report the results in Table 7. The results indicate the transmission from HYBX to oil prices being sensitive to structural breaks since the null hypothesis of no-transmission cannot be rejected. This alternate approach, which controls for gradual structural breaks indicates no information flow from high-yield bonds to energy prices. On the other hand, the transmission from oil prices and ethanol prices to HYBX remain evident even if we control for those gradual shifts. Thereby, the role of energy markets on high yield bonds seems to be robust to structural changes (of any type) in the series. 25

26 Table 7: Results from Fourier Toda-Yamamoto price transmission test with single frequency HYBX Energy Prices Energy prices HYBX k p Wald χ 2 -pval B-pval Wald χ 2 -pval B-pval Oil *** N. Gas Ethanol *** Notes: Toda and Yamamoto (1995) price transmission test results with Fourier approximation and single frequency are reported in the table. > denotes the null hypothesis of no-transmission. Maximum k and p are respectively set to 3 and 12, then optimal k and p are determined by Akaike information criterion. χ 2 -pval denote the chi-square p- values of the Wald test statistics. Bootstrap p-values (B-pval) are based on 1,000 replications. Fourier TY test with single frequency is based on equation (6). *** indicates statistical significance at 1 percent. According to our Monte Carlo simulations, the Fourier TY test with cumulative frequencies is more reliable when the sample size is larger. To follow suit, we incorporate cumulative frequencies in the testing procedure and compare with the single frequency analysis. As the results in Table 8 show, the relationships identified with the transmission analysis using cumulative frequencies are the same as the ones which used a single frequency. This finding can be interpreted as even a strong evidence of information flow from the energy markets to high yield bonds. Table 8: Results from Fourier Toda-Yamamoto price transmission test with cumulative frequency HYBX Energy Prices Energy prices HYBX k p Wald χ 2 -pval B-pval Wald χ 2 -pval B-pval Oil *** N. Gas Ethanol *** Notes: Toda and Yamamoto (1995) price transmission test results with Fourier approximation and cumulative frequency are reported in the table. > denotes the null hypothesis of no-transmission. Maximum k and p are respectively set to 3 and 12, then optimal k and p are determined by Akaike information criterion. χ 2 -pval denote the chi-square p-values of the Wald test statistics. Bootstrap p-values (B-pval) are based on 1,000 replications. Fourier TY test with cumulative frequencies is based on equation (5). *** indicates statistical significant at 1 percent. 26

27 As a summary, our results show the importance accounting for structural shifts as a gradual processes via the Fourier approximation. This approach is not only shown to be more robust than the traditional approaches, but also have significant implications on the results. As for our study, the traditional approach results indicate an information transfer from HYBX to oil prices; however, this relationship disappears when we account for gradual structural shifts. In addition, the new approach further confirms the uni-directional price transmission between the oil/hybx and ethanol/hybx. IV. C Volatility transmission analysis To investigate whether there is a volatility transmission between high-yield bonds and energy prices, we benefit from a relatively new LM-GARCH test proposed by Hafner and Herwartz (2006). The test is comparatively simple to implement because it is based on estimating a GARCH(1,1) specification and doesn t suffer from the short comings of traditional transmission tests (as previously explained in the methodology section). Essentially, these tests try to investigate whether historic volatility information in one variable has any predictive power of the volatility in another variable. In order to conduct our volatility tests, we first estimate the univariate GARCH (1,1) models for the series. Before proceeding to the inferences from the estimation, one needs to check whether the stability conditions (constant 0, the ARCH parameter 0, the GARCH parameter 0, and 1) of the GARCH model are satisfied. The results reported in Table 9 clearly indicate that the estimated GARCH models for all the variables satisfy the stability conditions. Furthermore, some inferences regarding the nature of the volatility of the variables can be drawn from these statistics. 27

28 The larger values for the ARCH and GARCH parameters increase the conditional volatility in different ways. A larger ARCH parameter implies the effects of a shock being more pronounced in the subsequent period. In comparison, a larger GARCH parameter implies the effects of a shock being more persistent (Enders, 2004). Therefore, while the larger ARCH parameter implies high short-run volatility, the larger GARCH parameter indicates a high long-run volatility. Our results show that the volatility processes of the energy prices and high-yield bonds to be dominated by the GARCH effect and the volatility behavior of the oil and natural gas prices to be very similar in nature. The ethanol prices and the high-yield bond index appear to have a different volatility path than oil and natural gas markets because of larger ARCH and smaller GARCH effects. The degree of persistence ( +β) indicates the persistence of the volatility shocks in all the variables. This finding implies that the conditional variance displays more autoregressive persistence, which further supports the evidence for the long-run volatility (Nazlioglu et al., 2013). Table 9: Results for variance equations Constant ARCH effect GARCH effect prob. prob. prob. HYBX 8E Oil 3E Natural Gas 1E Ethanol 9E Notes: The variance equation in GARCH(1,1) form is σ t = ω + αε t 1 + βσ t 1 where is the constant term, α is the ARCH effect and β is the GARCH effect. Higher αindicates high short run volatility. Whereas a higher β points out a higher log run volatility. (α+β) is a measure of volatility shock persistence. The coefficient estimates along with the p- values are reported in the table. All terms in the variance equation are significant at the 1% level. HYBX and ethanol have high short run volatility and relatively lower persistence, whereas oil and natural gas exhibit high long run volatility and relatively higher persistence. 28