Temporal dynamics of volatility spillover: The case of energy markets

Transcription

1 Temporal dynamics of volatility spillover: The case of energy markets Roy Endré Dahl University of Stavanger Norway Stavanger roy.e.dahl@uis.no Muhammad Yahya University of Stavanger Norway Stavanger muhammad.yahya@uis.no Atle Oglend University of Stavanger Norway Stavanger atle.oglend@uis.no Sindre Lorentzen University of Stavanger Norway Stavanger sindre.lorentzen@uis.no Abstract This paper examines the volatility spillover between the futures markets of five energy related commodities using daily data over the period from July 2001 to June Following Diebold and Yilmaz (2009, 2012) methodology (hereafter: DY), we show that spillover between energy commodities are relatively stable over time. However, during the periods of financial and economic turmoil, the spillover increases significantly. Our findings indicate bidirectional spillover in energy commodities, which is consistent with the findings of Asche et al. (2012), indicating a long-run relationship between the energy markets. Additionally, in harmony with the mainstream literature, our findings indicate that spillover from crude oil significantly affects the volatility in other energy commodities. Finally, our findings indicate that heating oil plays a significant role as well in volatility spillover in energy markets. Jel-Codes: Q02, Q41 Keywords: Volatility spillover, energy commodities, crude oil, transmission shocks 1

2 1 Introduction Volatility spillover has been a debated topic in financial and commodity literature throughout the last decades. Understanding the dynamics of time-varying spillover is crucial asset valuation, risk management, and policymaking (see e.g. Karyotis and Alijani, 2016; Belousova and Dorfleitner, 2012). Interestingly, relatively less attraction has been given to the field of volatility spillover (Nazlioglu et al., 2013). In this study, we examine the volatility spillover between energy commodities, namely, crude oil WTI (CL), natural gas (NG), coal (QL), gasoline (RB), and heating oil (HO). Specifically, we add to the existing literature by estimating the bidirectional static and temporal volatility spillover dynamics between the energy commodities by incorporating daily data from 2001 to The phenomenon of volatility spillover is time-varying and therefore the recent decline in oil price further necessitate the evaluation of volatility spillover between the energy commodities. Historical literature indicates that large swings in the crude oil prices are often followed by an increase in other commodity prices (Nazlioglu et al., 2013), raising question of whether the change in crude oil prices shift the temporal dynamics of other energy commodities. The more recent studies of Kang et al. (2017) and Zhang (2017) reports that crude oil is a net receiver of return and volatility spillover, which further questions the importance of crude oil as dominant commodity. The key limitation in the previous literature might be due to the choice of empirical methodology. Existing literature on volatility spillover is mainly constrained to application of multivariate generalized autoregressive conditional heteroscedastic models (MGARCH) to analyze the crossdynamics of volatility transmission. However, a key limitation of MGARCH is its inability to provide the directional spillover. To overcome this limitation, we apply a methodology proposed by Diebold and Yilmaz (2009, 2012). DY is based on a variance decomposition of forecast errors (FEVD) obtain from a generalized vector autoregressive model (VAR). The main aim of our study is to first empirically investigate the historical claim of volatility transmission from crude oil, being the dominant commodity, to the changes in volatility dynamics of other commodities. Specifically, we seek to answer whether the crude oil price really matters, and to what degree does the changes in price dynamics of crude oil shifts the equilibrium in other energy commodity prices. Secondly, as pointed by Asche et al. (2012), it is important to understand the development of relationship between natural gas and coal, because natural gas is often considered a substitute to coal. Therefore, investigation of this relationship is of special interest. The remainder of this article is structured as follows. In section 2 we present previous literature relevant for volatility spillover in the commodity market. The empirical methodology is presented in and the dataset is presented in section 3 and 4, respectively. The obtained empirical results are presented and discussed in section 5. Section 6 concludes. 2 Literature review Several studies have investigated the dynamics of oil price change and its effect on other assets. The increase in commodity prices since 2005 has renewed interest among researchers to identify the dynamics of volatility transmission in commodity markets. The spillover between crude oil and equity markets, between energy commodities, cross-market linkages between the crude oil and precious metals, and between crude oil and agricultural commodities have been the main focus of the recent studies. However, the empirical findings of these studies provide mixed evidence regarding the importance of crude oil as a dominant asset in volatility transmission. Malik and Hammoudeh (2007) examines the shock and volatility transmission by applying a multivariate GARCH model with BEKK parametrization using daily data from 1994 to 2001 between 2

3 the U.S. equity market, global crude oil market, and the equity markets of Saudi Arabia, Kuwait, and Bahrain. Their findings suggest that in all cases the Gulf markets receive volatility from the oil market with exception of Saudi Arabia, which is found to be a significant transmitter of volatility to the oil market. In a recent study, Diaz et al. (2016) investigates the relationship between the stock returns in the G7 economies and the oil price volatility by employing a VAR model using monthly data over the period of 1970 to Their findings indicate a negative response of G7 stock markets to an increase in oil price volatility. Additionally, their findings suggest that national oil price volatility is less significant than the world oil price volatility. Recently, Liu et al. (2017) examines the evolution of volatility spillovers between oil and stock market data of S&P 500 index and the MICEX index (Russia) by using daily frequency for the period 2003 to Using a wavelet-based GARCH BEKK method they show that the spillover relationship between oil and the U.S. market is short-term while the spillover relationship between oil and Russian stock market is dynamic relative to time scale. Table 1: Spillover between crude oil and stock markets Study Assets/Markets Data Method Results Malik and U.S. equity market, crude MGARCH Significant Hammoudeh (2007) oil, and Gulf markets (Daily) Diaz et al. (2016) Crude oil and stock returns in G7 countries (Monthly) VAR Insignificant Liu et al. (2017) Crude oil, MICEX, and S&P 500 (Daily) GARCH BEKK Insignificant Baffes (2007) Crude oil and other commodities (Annual) OLS Significant Serra (2011) Crude oil, ethanol, and sugar prices in Brazil (Weekly) GARCH Significant Kaltalioglu et Oil price, agricultural co al. (2011) mmodities and food items (Monthly) VAR Insignificant Lin and Li (2015) Crude oil and VECM natural gas markets (Monthly) MGARCH Significant Kang et al. (2017) Crude oil, gold, silver, corn, wheat, and rice (Weekly) DY (2009, 2012) Insignificant Notes. Significant indicates if a study finds crude oil has positive effect, and vice versa for insignificant. Mixed reflects bidirectional volatility spillover between the commodities. Baffes (2007) examines the spillover between crude oil and 35 internationally traded commodities using annual data from 1960 to 2005 and finds significant spillover from crude oil to other commodities. Serra (2011) examined the volatility spillover using a semi parametric GARCH model for crude oil, ethanol and sugar prices in Brazil using weekly data from 2000 to His findings suggest that the ethanol and crude oil, as well as ethanol and sugar price levels are linked in the long-run by an equilibrium parity. In their study, Kaltalioglu et al. (2011) investigate the spillover between oil, agricultural raw material price indexes, and food consumption items using monthly data from 1980 to Their findings indicate that the dynamics of oil prices does not Granger cause the variance in agricultural and food raw material prices. Further, they found bidirectional spillover between food markets and the agricultural raw material. Lin and Li (2015) incorporated a vector error correction model (VECM) with a MGARCH model to evaluate the price and volatility spillover between crude oil and natural gas markets in the U.S., Europe and 3

4 Japan. Their findings indicate spillover from crude oil markets to natural gas markets. In a later study, Kang et al. (2017) examine the volatility spillover between six commodity futures markets (gold, silver, crude oil, corn, wheat, and rice) by employing a multivariate DECO GARCH model and the spillover index using weekly data from 2002 to Their findings indicate bidirectional return and volatility spillovers between commodity futures markets. To summarize, regardless of theoretical underpinnings, the empirical findings of these studies provide mixed evidence regarding the importance of crude oil as a dominant asset in volatility transmission. The direction and intensity of spillover between energy commodities prices is opaque and suggests the need for further investigation. Therefore, in this paper, we fill the gap by estimating the temporal dynamics of volatility spillover between these commodities. 3 Methodology Following Diebold and Yilmaz (2012, 2009), we briefly present the utilized methodology to quantify the directional spillover in generalized VAR models. Consider a generalized vector autoregressive (VAR) model to conduct a variance error decomposition. Let a set of data N variables, which are covariance stationary be represented by a VAR(p) model of the following specification: p x t = φ i x t i + ε t where ε (0, σ) (1) i=1 Next, we decompose variance of residuals obtained from the generalized VAR model i.e. let the H-step-ahead FEVD be given as: σ θ g ii 1 ij (H) = H 1 (e i A h ej ) 2 h=0 H 1 h=0 (e i A h A h e j), (2) where θ g ij (H) is forecast error variance decomposition, is variance matrix, σ ii is standard deviation of the error term, and e i is selection vector with one as the ith element and zeros otherwise. Equation 2 provides a spillover index of N N matrix. Each element of this matrix represents the contribution to/from asset j to the forecast error variance asset i. θ g ij (H)) = θg ij (H). (3) θ g ij (H) j=1 The total volatility spillover index is produced using the volatility contributions from variance decomposition: θ g ij (H) θ g ij (H) S g (H) = i,j=1 i j i,j=1 θ g ij (H) 100 = i,j=1 i j N 100 (4) Equations 5 and 6 provide an estimate of the directional volatility spillovers from asset i to all other markets j as follows: S g i (H) = j=1 i j j=1 θ g ij (H) θ g ij (H) 100 = j=1 i j θ g ij (H) N 100 (5) 4

5 S g i (H) = j=1 i j j=1 θ g ji (H) θ g ji (H) 100 = j=1 i j θ g ji (H) N 100. (6) The net spillover is the difference between shocks transmitted and received. The net spillover from the asset i to all other assets j can be obtained by subtracting equation 6 from 5 as: S g i (H) = Sg i (H) Sg i (H). (7) For further understanding of the underlying methodology, we refer the interested reader to Diebold and Yilmaz (2009, 2012). 4 Data and descriptive statistics Our data set consist of commodity nearby futures prices. The sample contains five commodities with 3,737 observations each, which exhibits a daily closing price timespan from to The selected period enables us to evaluate how the decline in oil price changes the return and volatility spillover dynamics between the energy commodities. The use of daily frequency data would enable us to take into account the day-of-the-week effect, prevalent in many time series data. Usage of weekly or monthly frequency observation would not able to capture this effect. The data chosen is extracted from the Commodity Research Bureau (CRB). Based on data availability, we select a total number of five commodities from energy sectors: Heating oil, Crude oil, Gasoline, Coal, and Natural gas. Figure 1 shows continuously compounded returns and the development in daily spot prices for all commodities in the sample. The price series are upward trended post-2005 and peaked during 2008, which is followed by a decline due to the global financial crisis in 2008 (GFC). This can be associated with the higher risk of assets during the financial and economic turmoil. In addition, visual inspection suggest that all energy commodities are stationary at first difference and non-stationary in levels. Furthermore, the return series appears to reflect volatility clustering with periods of tranquility and turmoil. 5

6 Figure 1: Development in commodity spot prices and returns: (a) Heating oil (b) Crude oil price return 1/1/2002 7/1/2005 1/1/2009 7/1/2012 1/1/ price return 1/1/2002 7/1/2005 1/1/2009 7/1/2012 1/1/ (c) Gasoline (d) Coal price return price return /1/2002 7/1/2005 1/1/2009 7/1/2012 1/1/2016 1/1/2002 7/1/2005 1/1/2009 7/1/2012 1/1/2016 (e) Natural gas price return /1/2002 7/1/2005 1/1/2009 7/1/2012 1/1/2016 We calculate the continuously compounded daily return for each commodity as the difference in logarithms of two consecutive prices at time t and t 1: r i,t = ln(p i,t /P i,t 1 ). Table 2 shows descriptive statistics of the daily log-return series on spot prices for the 5 commodities and the results of statistical tests. 1 As it can be seen from the table, average annual return ranges between -5% to 5% and exhibits a standard deviation between 24% and 73% for coal and natural gas respectively. In terms of reward-to-risk measure, heating oil provides highest return in proportion 1 Mean and standard deviation is annualized by multiplying each with 252 and 252, respectively. 6

7 to risk. Overall, preliminary findings indicate all the return series exhibits skewed and leptokurtic distributions. Based on the third and fourth order moment of the statistical distribution, there are strong indications of deviation from a normal distribution. A formal Jarque-Bera (JB) normality test is able to reject the null-hypothesis of normality for all commodities. Majority of the log-returns exhibit a negative autocorrelation. The Ljung-Box portmanteau test for white noise rejects the null-hypothesis for several of the commodities, thus showcasing that the observed autocorrelation is significant. This indicates that the past return contains information that is relevant for future return forecasting. Table 2: Descriptive statistics of daily log returns Commodity Mean Std dev Skew Kurtosis Min Max JB AC Heating oil (0.03) Crude oil (0.00) Gasoline (0.29) Coal (0.00) Natural gas (0.00) Notes: Annualized figures of mean and standard deviation are presented. Skew refers to skewness. JB refers to the p-value from a Jarque-Bera normality test and AC is the first order autocorrelation coefficient with p-value from Ljung-Box portmanteau test for white noise in parenthesis. Table 3 reports the unit root tests result for level and logarithmic returns by applying Augmented Dickey-Fuller (ADF) (Dickey and Fuller, 1979) and Phillips-Perron (PP) (Phillips and Perron, 1988) unit-root tests. Both the ADF and PP test with and without deterministic trend is utilized. The null hypothesis of unit-root was not rejected at levels, but rejected in returns, which indicates that all the return series follow an I(1) process. Table 3: Test for stationarity in commodity prices Commodity ADF PP ADF PP Trend No trend Trend No trend Trend No trend Trend No trend Price Return Heatingoil Crudeoil Gasoline Coal Natural gas Notes. Augmented Dickey-Fuller (ADF) (Dickey and Fuller, 1979) and Phillips-Perron (PP) (Phillips and Perron, 1988) unit-root tests for stationarity both with and without deterministic trend. The p-values from both tests are reported in the table. 5 Empirical analysis Based on the log-returns ( p t ) of the evaluated commodity prices, we fit a VAR(1) model in order to obtain the residuals for later 100-days-ahead forecast of generalized errors variance decomposition. The estimates might be sensitive to lag length. We analyze the robustness of our estimates to different model specifications. As shown by Diebold and Yilmaz (2012), in order for DY methodology to hold, the VAR model should be covariance-stationary. Table 3 in Section 4 shows that all variables are first difference stationary. Applying the DY methodology to the VAR model, we obtain a (5 5) matrix of directional spillover (θ g ij (H)). Based on the matrix of directional spillover, we derive four additional statistics, g namely, the gross directional spillover to commodity i (Si (H)), the gross directional spillover from 7

8 Table 4: Volatility spillover between energy commodities To/From (a) Spot: Heating Crude Natural Sum Gasoline Coal oil oil gas (Excl.) Heating oil Crude oil Gasoline Coal Natural gas Sum (Incl.) Sum (Excl.) Net spillover Total Spillover Index: 40.17% Notes: The underlying variance decomposition is based on VAR(1) model. Table shows all the possible bivariate relations of directional volatility spillover between energy commodities. The diagonal entries (S g ii (H)) of the table shows self-caused volatility. The net spillover (S g i (H)) is informative of whether the given commodity tend to receive or transmits volatility. The total spillover index (S g (H)) can be approximated through the ratio between row sum (excl.) and row sum (incl.). commodity i (S g i (H)), the net spillover for commodity i (Sg i (H)), and the total volatility index (S g (H)). Each diagonal entry (S g ii (H)) represents the self-caused volatility within the given asset when spillover is extracted from the total volatility. For instance, 39.53% and 86.1% of the Table 4 is self-caused volatility of heating oil and coal, respectively. The column, sum (excl. diagonal entries), displays the volatility received by the given commodity. For instance, the gross directional g volatility spillover to gasoline from all other commodities is 58.71%, Si (H) (see Equation. 5). The row, sum (excl. diagonal entries), provides an estimate of volatility spillover transmitted by a given commodity to all other commodities, which is the gross directional volatility spillover from commodity i to other commodities, S g i (H) (see Equation. 6). For example, on aggregate, crude oil transmits in total 67.22% to other energy commodities. The net spillover (S g i (H)) (see Equation. 7) is the difference between the row sum (excl.) and column sum (excl.), which is informative of whether a given commodity tend to receive more volatility than it transmits. For instance, coal has a net volatility spillover of 6.89% (= 7.01% 13.9%) thus indicating coal as net receiver of volatility from other commodities. The average spillover between the commodities, the total volatility index (S g (H)), can be approximated through the ratio between the row sum (excl.) and row sum (incl.) (see Equation. 4). The average spillover between the energy commodities is 40.17%. This statistic indicate that the volatility of a given energy commodity significantly depends on other commodities within the energy sector. The static volatility index provides an estimate of overall spillover between assets, and therefore does not provide any information about the change in volatility spillover over time. We study the net directional spillover, spillover between commodities, and total volatility spillover index using rolling sample analysis. The rolling estimates will enable us to understand the development of behaviors and relations between the commodities over time. We choose a rolling-window of 252-days (1-year) observations to analyze the volatility spillover. Figure 2 shows the time-variant development in temporal dynamics of gross directional volatility spillover to each commodity over the sample period. Occasional spikes can be observe during the periods of financial turmoil causing the volatility spillover to increase significantly. Additionally, 8

9 Figure 2: Directional spillover to commodity i: (a) Heating oil (b) Crude oil Gross directional spillover to heating oil Gross directional spillover to crude oil β = p value = 0.00 R 2 = 0.19 N = 3485 ADF: p value = 0.19 PP: p value = 0.19 β = p value = 0.00 R 2 = 0.42 N = 3485 ADF: p value = 0.92 PP: p value = 0.91 (c) Gasoline (d) Coal Gross directional spillover to gasoline β = p value = 0.00 R 2 = 0.23 N = 3485 ADF: p value = 0.49 PP: p value = 0.54 Gross directional spillover to coal β = p value = 0.00 R 2 = 0.03 N = 3485 ADF: p value = 0.73 PP: p value = 0.70 (e) Natural gas Gross directional spillover to natural gas β = p value = 0.00 R 2 = 0.04 N = 3485 ADF: p value = 0.16 PP: p value = 0.21 negative trend and intensity of volatility spillover to each energy commodity is apparent since the decline of oil price. These findings indicate that the net spillover between the energy commodities is non-stationary and changes during the sample period, and crude oil became increasingly more exogenous as the gross spillover to crude is trending downward. Analogously, Figure 3 shows the development of net volatility spillover to commodity i from other commodities. Consonant to gross volatility spillover, the findings Figure 3 displays continuously changing pattern of spillover. In accordance to the findings of static full-sample analysis of Table 9

10 Figure 3: Net spillover between commodities: (a) Heating oil and Crude oil (b) Heating oil and Gasoline Pairwise spillover between heating oil and crude oil β = p value = 0.00 R 2 = 0.53 N = 3485 ADF: p value = 0.85 PP: p value = 0.86 Pairwise spillover between heating oil and gasoline β = p value = 0.00 R 2 = 0.13 N = 3485 ADF: p value = 0.10 PP: p value = 0.11 (c) Heating oil and Coal (d) Heating oil and Natural gas Pairwise spillover between heating oil and coal β = p value = 0.37 R 2 = 0.00 N = 3485 ADF: p value = 0.39 PP: p value = 0.32 Pairwise spillover between heating oil and natural gas β = p value = 0.00 R 2 = 0.41 N = 3485 ADF: p value = 0.77 PP: p value = 0.72 (e) Crude oil and Gasoline (f) Crude oil and Coal Pairwise spillover between crude oil and gasoline β = p value = 0.00 R 2 = 0.24 N = 3485 ADF: p value = 0.72 PP: p value = 0.82 Pairwise spillover between crude oil and coal β = p value = 0.02 R 2 = 0.00 N = 3485 ADF: p value = 0.57 PP: p value = 0.59 (g) Crude oil and Natural gas (h) Gasoline and Coal Pairwise spillover between crude oil and natural gas β = p value = 0.00 R 2 = 0.33 N = 3485 ADF: p value = 0.48 PP: p value = 0.42 Pairwise spillover between gasoline and coal β = p value = 0.00 R 2 = 0.01 N = 3485 ADF: p value = 0.34 PP: p value =

11 Figure 4: Pairwise spillover between heating oil and other energy commodities: (a) Gasoline and natural gas (b) Coal and Natural gas Pairwise spillover between gasoline and natural gas β = p value = 0.00 R 2 = 0.46 N = 3485 ADF: p value = 0.29 PP: p value = 0.33 Pairwise spillover between coal and natural gas β = p value = 0.00 R 2 = 0.02 N = 3485 ADF: p value = 0.09 PP: p value = 0.08 (c) Total Volatility Index Total volatility spillover (%) β = p value = 0.00 R 2 = 0.14 N = 3485 ADF: p value = 0.84 PP: p value = , the rolling window estimates illustrates that the crude oil became increasingly more important in changing the dynamics of return and volatility of other commodities in the energy sector. Net spillover of crude oil shows that crude oil transmits less than it receives from other energy commodities. However, the net spillover is increasing over time in the terms of spot prices. In the case of total volatility index Panel c of Figure 4 shows that the volatility spillover increases significantly during the period of turmoil. The highlighted region displays the period of financial crisis (2008), two European debt crisis (2010 and 2012, respectively), and the decline in crude oil prices ( ). Figure (b) is the net spillover between coal and natural gas. A gradual upward trend is apparent, which is augmented by the transitory spikes of increased connection between 11

12 these two commodities. Total volatility index is negative, reflecting over time decrease in total volatility spillover between the energy commodities. 6 Conclusion Previous research on volatility spillover provides mixed evidence regarding importance of crude oil as dominant commodity in changing the price and return equilibrium of other commodities and assets. Several studies find no linkage between crude oil and other assets. Through our analysis, we show that most of the energy commodities are connected through volatility spillover. Due to increased interconnectedness of global financial and commodity markets, understanding the temporal dynamic link between the energy commodities is of particular importance to policymakers, regulatory agencies, and market participants. There are several noteworthy findings. First, the amount of spillover is time-variant and appears to be decreasing throughout the sample period. Additionally, the short-term events tends to have major influence on volatility spillover, which can explain the discrepancy in previous findings of volatility spillover from previous literature. Second, not all commodities are equally important. For instance, crude oil is a large net transmitter while coal is a net receiver. Third, during the period of financial and economic turmoil, the total volatility spillover between the energy commodities significantly increases. Finally, contrary to ex-ante expectations, there is no or little connection between coal and natural gas on average. However, taking the time-varying property of this relation into account, there are periods of increased spillover between coal and natural gas. 12

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