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  1. 1. Accepted by International Conference on Management Science and Engineering, May 2009 1 Dynamic Correlation between Carbon Market and Chinese Stock Market Based on AGDCC-GARCH LU Wei, WANG Wen-jun School of Management, University of Science and Technology of China, P.R.China, 230026 Abstract: Along with the worldwide concern on allowance-based trading, the baseline-and-credit trading climate change, the greenhouse gas emission permit has is project-based, in which sources receive tradable emerged as a new asset with increasing liquidity and its credits from projects that can be certified to reduce derivatives has been traded more and more frequently on greenhouse gas emissions compared with a baseline climate exchanges. This paper selects the European project. The typical example of this kind of trading is the Union Allowance (EUA) futures traded on European Clean Development Mechanism (CDM), in which the Climate Exchange (ECX) to represent the emission credits are called Certified Emission Reduction (CER). permit market (carbon market), Shanghai Composite One unit of EUA and CER permits the holder to emit one Index to represent Chinese stock market, and adopts the ton of carbon dioxide. The common of cap-and-trade and Asymmetric Generalized Dynamic Conditional baseline-and-credit trading is that they are both Correlation (AGDCC) - GARCH model to analyze the developed to help countries that have compulsory dynamic correlation between carbon market and Chinese emission reduction tasks in Kyoto Protocol. The third stock market. The empirical result shows that, the EUA kind of carbon trading differs in that it involves futures share the characteristics of “Heavy Tail” and voluntary emission reductions. The Chicago Climate “Volatility Clustering” with conventional financial Exchange (CCX) is the largest platform for the voluntary assets, and are correlated very weakly with the Shanghai emission trading, in which some plants and authorities Composite Index. Moreover, the correlation becomes make voluntary emission reduction commitments, which even weaker when the volatility in Shanghai Composite can be met by reducing emissions inside the organization Index increases. The results have important significance or buy allowances and credits from the cap-and-trade and for Chinese investors to seize the opportunity brought up project-based system. by carbon market to make internationally diversified investments. 1.2 The trading of carbon assets Keywords: European Union Allowance (EUA) More and more trading have carbon assets involved. futures, AGDCC - GARCH, Correlation, Volatility According to the report by World Bank in May, 2008, the volume and market value of carbon market has greatly 1 Introduction grown since its foundation in 2005[1]. The volume was 0.71 billion tons of CO2 equivalent (CO2e) in 2005, 1.745 1.1 A brief introduction of the greenhouse gas billion in 2006 and 2.983 billion in 2007. The market emission permits trading market (carbon market) value increases in a faster rate with the rise of prices, The greenhouse gas emission permits trading from 10.864 billion dollars in 2005 to 31.235 billion in market is usually called carbon market for short. Since 2006 and 64.035 billion in 2007. The secondary market carbon dioxide is the largest agent of global warming, for project-based trading has also been developed. Take other kinds of greenhouse gas are measured in the CO2 secondary CER for example. The volume of secondary equivalents according to their one-year Global Warming CER trading was 0.025 billion tons in 2006, increasing to Potential. Thus, the greenhouse gas emission permits 0.24 billion in 2007, with the market value increased measured in CO2 equivalents are all called carbon assets. from 0.445 billion dollars in 2006 to 5.451 billion in Since the Kyoto Protocol came into effect in Feb.16, 2007. Besides, the trading of derivatives of carbon assets 2005, the trading of carbon assets has grown widely grows even faster than the underlying assets. Especially around the world. in the EU ETS, most of the trading are in the form of There are now three kinds of carbon trading on futures contracts, while the spot trading only accounts for current carbon market: cap-and-trade, baseline–and- 2% of the volume and less than 1% of the market value. credit and voluntary trading. The cap-and-trade is also The exchanges specializing in carbon trading have been called allowance-based trading, in which a maximum established around the world, provide kinds of limit on emissions (i.e. allowances) is set by authorities derivatives of the carbon assets and make great and sources covered by the system is authorized to emit contribution to the enhancement of the market liquidity. in the form of emission allowances. Those who emit For example, the European Climate Exchange (ECX) more than the cap have to buy allowances from those located in Amsterdam offers futures and options of EUA who emit less than the cap. A typical model of this kind and CER respectively. of trading is the European Union Emission Trading With the development of carbon market, Scheme, in which the emission allowance is called participators in the market become diversified. Besides European Union Allowance (EUA). Different from the those who want to use the trading to meet their
  2. 2. Accepted by International Conference on Management Science and Engineering, May 2009 2 obligation in Kyoto Protocol, more and more traders are believed to be able to depict the heteroskedasticity and intermediaries with the purpose of risk management and volatility clustering of the returns of financial assets and profit seeking. A major part of the traders are financial has become the most commonly used model in volatility institutions, providing services in project financing, measurement. It has been extended to various types such delivery guarantee, carbon asset portfolio management as GARCH-M, GJR, EGARCH, IGARCH and has and carbon derivatives. These financial services not only formed a large family of GARCH models. provide liquidity to the market but also enhance the To study the volatility spillover effects among more diversification on carbon market. than two assets, multivariate GARCH models have been developed but raise problems in the parameter estimation 1.3 The aim and significance of this study due to the increased complexity (Fan & Zhang,2003[4]) . With the development of greenhouse gas emission Thus, the model estimation methods for GARCH family permit trading market (i.e. the carbon market), the models have been developed. Bollerslev , Engle & market liquidity has been enhanced and the greenhouse Woodridge(1988) [5] suggested the VECH-GARCH gas emission permits (i.e. carbon assets) have become a model, which simplifies the multivariate model but was new form of asset. As the world’s continuing attention on not able to ensure that the conditional variance matrix is climate change, it can be expected in the near future that a positive definite matrix. The constant conditional greenhouse gas emission trading will be developed all correlation (CCC) model proposed by Bollerslev (1990) around the world and the trading of carbon assets will [6] succeeded in reducing the number of the parameters in see breakthroughs in terms of both size and form. the model but was not able to describe the time-varying Therefore, the carbon assets, representing the right of correlation. The BEKK model developed by Engle & greenhouse gas emission, will become an important Krone(1995)[7] succeeded in ensuring that the conditional global asset, raise new investment opportunities and variance matrix is a positive definite matrix but could not should be used in internationally diversified investments. be reasonably explained by economic theories. It is believed that, the correlation among assets is an After the CCC model, Engle (2002) [8] developed important factor to impact the risk and return of a the Dynamic Conditional Correlation (DCC) model, portfolio. The aim of this study is to analyze the which is able to describe the time-varying correlations correlation between carbon market and Chinese stock and can be explained reasonably by economic theories. market and then provide references for Chinese investors The major breakthrough in DCC is to use a two-step to invest in carbon assets, which is of important estimation method to overcome the computation significance for Chinese investors to use carbon market complexity involved in the parameter estimation of to diversify risk and increase revenue. multivariate GARCH models, in addition to come up So far, few academic researches have addressed the with a consistent estimation of the time-varying issue of correlation between carbon assets and other correlation matrix (Engle, 2002[8]). Moreover, in DCC, forms of assets. R. Kosobud, H. Stokes, C. Tallarico, and any type of GARCH family models with stationary B. Scott (2005)[2] calculated the linear correlation covariance and normally distributed errors can be used to between SO2 emission quotas in the United States and model the volatility of the return rate of a certain single NASDAQ, S&P 500, Russell 2000 & 3000 and risk-free asset. Thus, DCC is more flexible in modeling the Treasury respectively. A limit in their study is that they volatility of asset return rates and is favorable for getting only calculated the linear unconditional correlation the most accurate model to describe the volatilities. DCC coefficient instead of considering the time-varying is used widely in international financial research on correlation. To describe the time-varying correlation, this correlation measurement (e.g. Colm Kearney &Valerio study uses the Asymmetric Generalized Dynamic Potì(2006)[9], Anders C. Johansson(2008)[10] , Liu & Conditional Correlation (AGDCC) model to calculate Zhang(2005)[11], Zhou & Pan(2006)[12], Gu & Lu(2006) time-varying correlation coefficient between carbon [13] , Zhen & Zhang(2007 a)[14] etc.). market and Chinese stock market. This study fills the gap To take into account the asymmetric responses of of only linear correlations are considered in previous assets correlation to positive shocks and negative shocks, studies. Also, this study is the first study to examine the that is, the assets correlation tends to increase more when correlation between carbon market and stock market. there are negative shocks to the asset prices than that when there are positive shocks, Cappilello, Engle & 2 Literature review and the model Shepard (2006) [15]generalized DCC to Asymmetric Generalized Dynamic Conditional Correlation 2.1 Literature review (AGDCC). AGDCC has been affirmed to be better than In finance, the correlation among various financial other GARCH models by Chinese scholars in their recent markets is an important issue in capital market research. studies. For example, Zhen & Zhang (2007) [16] examined The first step to measure the correlation is to describe the to correlation among major stock indices in China using return and volatility of the assets. The Generalized AGDCC and concluded that AGDCC is better in Autoregressive Conditional Heteroskedasticity forecasting than other GARCH-family models. Qin & (GARCH) model proposed by Bollerslev(1986) [3] are Zhen (2008) [17] forecasted the correlations among Chinese stock indices and also concluded that AGDCC is
  3. 3. Accepted by International Conference on Management Science and Engineering, May 2009 3 better than others. Yuan, Zhang & Wang (2008) [18] adopts 1 T 1 T AGDCC in their study on the dynamic correlation calculated as Q = ∑ ε t ε t′ and N = T ∑ nt nt′ using T t =1 t =1 between stock market and bond market. Given the samples. When there are two assets, the parameter matrix successes of AGDCC model in empirical studies and the flexibility of AGDCC model in depicting the volatilities  a1 0  b1 0  can be written as: A =   , B = 0 b  , and correlations, this study selects AGDCC model to  0 a2   2 calculate the time-varying correlation coefficients of g 0 carbon market and Chinese stock market. G= 1  . It can be seen that AGDCC generalizes  0 g2  2.2 The model DCC in two dimensions: one is to allow the different The DCC model developed by Engle(2002)[8] impacts of assets on the dynamic correlation; the other is represents the time-varying correlation coefficient ρ12t to introduce a parameter to measure the impact of negative shocks, thus can be used to examine the as: ρ12,t = q12, t q11,t q22,t (1) asymmetric impact of positive shocks and negative and qij ,t = ρij + α (ε i ,t −1ε j ,t −1 − ρij ) + β (qij ,t −1 − ρij ) (2) shocks on the asset correlation. Through their empirical study on stock markets and bond markets in different in which ε t = (ε1t , ε 2t )′ are the standardized errors nations, Cappilello, Engle & Shepard (2006) [15] proves from the single variate GARCH models and ρij is the that AGDCC is superior to the ADCC model in which the parameter matrices degenerates to scalars and the unconditional correlation coefficient between the DCC model in which the asymmetry of positive and standardized errors. Let Qt = (qij ,t ) 2× 2 . The above negative shock is neglected. dynamic conditional correlation coefficient equation can be written in the form of variance-covariance matrix as: 3 Data and descriptive statistics Qt = S (1 − α − β ) + α (ε t −1ε t −1′ ) + β Qt −1 (3) According World Bank, EU ETS continues to play a  1 ρ12  and S = E (ε t ε t′ ) =   (4) major role on carbon market in 2007. In 2007, the  ρ12 1  trading volume of EUA was 2.061 billion ton, accounting The DCC-GARCH model in Engle (2002)[8] is for 69% of the total volume of carbon trading. The estimated by MLE. The logarithmic maximum likelihood market value of EUA trading was 50.097 billion dollars function of the model is: in 2007, accounting for 78% of the total amount on 1 carbon market. The first phase of EU ETS is 2005 to L = − ∑ (2 log(2π ) + 2 log( h1t h2t + 2007, while the second is 2008 to 2012, the same as the 2 t (5) commitment period of Kyoto Protocol. EUAs are (ε 2 + ε 2t − 2 ρt ε1t ε 2 t ) 2 allocated to sources according to the National Allocation log(1 − ρt2 ) + 1t ) (1 − ρt 2 ) Plans (NAPs) stipulated by the European Union. Those [8] Engle(2002) proposed to use a two-step estimation who are short of allowances need to buy EUAs from procedure to estimate the parameters. In the first step, the those with extra ones, or they will get punished by 40 standardized errors and conditional variances are euro per ton in the first phase and 100 euro per ton in the obtained. Then, in the second step, the parameters are second phase. Every year before April 30, the sources estimated through the logarithmic maximum likelihood need to hand in EUAs in the amount equivalent to its function. Engle (2002)[8] stated that, although the emissions in the previous year, which will be deducted estimation result from this two-step procedure is not from the total amount of allowances it holds in the phase. efficient but is consistent. Moreover, even the errors Most of EUA trading is in the form of futures from GARCH models are not normally distributed, the contract. The ECX and Nordpool both offer the EUA estimation result owns the characteristics of Quasi-MLE futures trading, more than 85% of which took place in estimation. ECX. ECX EUA futures are traded on ICE Futures The AGDCC model developed by Cappilello, Engle platform. To trade EUA futures on ICE Futures, the only & Shepard (2006) [15] extended Qt as: requirement is to become a member of ICE Futures or do deals through an intermediary that is an ICE Futures Qt = (Q − A′QA − B ′QB − G ′NG ) + A′ε t −1ε t −1′ A member. The trading hour is 7: 00—17: 00 UK local (6) + B ′Qt −1 B + G ′nt −1nt −1′G time. The futures are listed on a quarterly expiry cycle with March, June, September, December contract months in which A , B , G are diagonal matrix of the parameters such that 17 months will be listed from Dec.2008 to , G and nt are measurements for the asymmetry, Dec.2012. The December contracts are mostly traded. nt = I[ ε t < 0] o ε t , I is the indicator function and “ o ” This is because that the sources need to check its actual emissions with its allowance in the end of every means the Hadamard product. Q = E (ε t ε t′ ) and commitment year, thus the trading in December are more than those in other months in the year. N = E (nt n t′ ) are both unconditional means and are EUA futures with the expiry month in Dec. 2009 are
  4. 4. Accepted by International Conference on Management Science and Engineering, May 2009 4 The descriptive statistics of the returns are listed in 35.00 Tab. 1. It can be seen that, similar to financial assets, the 30.00 return of EUA futures also shows the characteristic of 25.00 “sharp peak and heavy tail”. The JB test rejects the 20.00 normality of the returns. The results of ADF test prove 15.00 the stationary of the two returns. 10.00 5.00 4 Results and discussion 0.00 2005- 2005- 2005- 2006- 2006- 2006- 2007- 2007- 2007- 2008- 2008- According to the two-step estimation method in 4-22 8-16 12-8 4-3 7-27 11-16 3-12 7-3 10-23 2-15 6-11 AGDCC, the first step is to develop GARCH model for Fig. 1: Prices of DEC09 EUA futures (2005-4-22 -2008-6-30) the volatilities of the asset return and then the second (Euro/ton) step is to obtain the value of parameters using MLE. The followings are the results in the twp steps. selected as the sample. EUA futures contract was launched on April 22, 2005. The prices of EUA futures STEP 1: Modeling the volatility of assets from then to June 30, 2008 are shown in Fig. 1. Engle (2002)[8] stated that any type of GARCH The highest price was 32.9 euro per ton while the model with stationary covariance and normally lowest was 12.8 per ton. It is obvious that the price distributed errors can be used to model the volatilities in slumped around late April 2006. The reason is that it was DCC. With reference to Cappilello, Engle & Shepard the first time that the sources disclosed their emissions in (2006) [15], here we use the Schwarz’s Bayesian Criteria 2005 and it turned out that there was supply surplus of (SBC) to select the best fitted GARCH model. EUAs, leading to the sharp decrease in price in one day on April 26, 2006. After that, the price showed much less (1) The return rates of EUA futures volatility and tended to increase after Feb. 2007. To The ACF and PACF of { d ln ct } show that the auto eliminate the impact of emerging trades before and at correlations and partial correlations of the sequence are April 26, 2006, this paper selects the samples from April not significant at any lag. Thus, { d ln ct } can be modeled 27, 2006 to June 30, 2008. The data of EUA futures are from the website of ECX and that of Shanghai { r1t } for ARCH- as: d ln ct = c1 + r1t . Test of the errors Composite Index are from Yahoo! Finance. Since there effect shows that there is ARCH effect in { r1t } , meaning has been little knowledge on EUA futures in China, the issue of the non-synchronous trading is neglected here. that { r1t } needs to be modeled using GARCH-family For the sake of the match of the samples, only the dates models. To test whether the impacts of positive shock with trading on both markets are retained in the sample. and negative shock on the volatility of the yields of EUA Finally, the sample size is 520. futures are the same, here the symmetric GARCH model Let { ct } denote the daily settlement price of EUA is used to be compared with the asymmetric GJR model and EGARCH model. The modeling results show that futures and { st } denote the daily settlement value of the terms showing the asymmetry in GJR and EGARCH Shanghai Composite Index. Then the return rates are are not significant at the significance level of 5%. d ln ct = 100 × [ Ln(ct ) − Ln(ct −1 )] (7) Moreover, the SBC values show that GARCH (1, 1) is and d ln st = 100 × [ Ln( st ) − Ln( st −1 )] (8) the best fitted model. Therefore, there is no difference between the impacts from positive shock and negative Tab. 1: Descriptive Statistics of the Return Rates of EUA shock on the conditional variance of the yields of EUA Futures and Shanghai Composite Index futures. The GARCH (1, 1) model for EUA futures yields is : h1t = c2 + c3 r1t −1 + c4 h1t −1 and the values of the 2 Shanghai EUA Futures Composite Index parameters are listed in Tab. 2. The conditional variances of EUA futures yields are shown in Fig.2. Average 0.1566 0.1268 Maximum 18.6526 8.8875 Tab.2: The estimated parameters in the mean-volatility Minimum -13.1868 -9.2562 model of EUA futures yields Sd. 2.6067 2.2678 c1 c2 c3 c4 Skewness 0.2925 -0.6678 Kurtosis 10.1662 4.9736 value 0.0952 0.4680 0.0750 0.8362 p-value of JB 0.0000 0.0000 p-value 0.2964 0.0005 0.0001 0.0000 Test AIC 4.573653 p-value of ADF 0.0000 0.0000 SBC 4.606423 Test
  5. 5. Accepted by International Conference on Management Science and Engineering, May 2009 5 .5 a1 b1 g1 a2 b2 g2 .4 0.1494 0 0.8505 0.5246 0.0837 0 14 .3 .2 12 .1 10 .0 8 -.1 6 -.2 4 2006M07 2007M01 2007M07 2008M01 2 Fig. 3: The time-varying conditional correlation coefficient 2006M07 2007M01 2007M07 2008M01 Fig. 2: The conditional variance of EUA futures yields Tab. 5: Descriptive statistics of the time-varying conditional correlation coefficient The parameters in GARCH (1, 1) are all significant Mean Median Max Min Sd. at 5% significance level, meaning that the volatilities of 0.10 0.11 0.42 -0.14 0.06 the yields of EUA futures are time-varying. It can also be seen from Fig. 2 that, the “volatility clustering”, which has often been observed in the yields of financial assets, is also presented in the yields of EUA futures. Tab. 5 shows that the correlation coefficient of EUA futures and Shanghai stock market is around 0.1, which (2) The return rates of Shanghai Composite Index is quite low compared with the correlation between { d ln st } can be modeled as: d ln st = c1 + r2t . For the conventional financial markets such as stock markets and bond markets. Moreover, the correlation coefficient volatility of the errors, the symmetric GARCH model is between the conditional correlation coefficient sequence also used to be compared with the asymmetric GJR and the conditional variance sequence of Shanghai model and EGARCH model. The modeling results show Composite Index is calculated to be -0.1317. Therefore, that the terms showing the asymmetry in GJR and when the volatility in Shanghai stock market increases, EGARCH are not significant at 5% significance level. the correlation of Shanghai stock market and EUA Moreover, the SBC values also show that GARCH (1, 1) market tend to decrease. This finding is opposite to those is the best fitted model. Thus, the GARCH (1, 1) model of the correlation of international stock market and for the yields of Shanghai Composite Index is: market volatilities in previous studies. Many researches h2t = c2 + c3 r22it −1 + c4 h2t −1 and the value of the parameters on international stock markets have found that the is listed in Tab. 3. correlation among international stock markets increases when the volatilities on the markets rise (e.g. Longin & STEP 2: Estimation of the time-varying correlation Solnik (1995) [19]; Chesnay & Jondeau (2000) [20]), which The values of the parameters in the dynamic results in that the performance of internationally correlation model are listed in Tab.4. It can be seen that, diversified investment turns worse when there are there are differences between the impacts of the volatility increased volatilities on the markets and there are on EUA market and Shanghai stock market on the increased needs for diversified investments. On the correlation. The large value of g1 shows that, the contrary, the findings of this study shows that, the negative shock on EUA market has more significant performance of diversified investment on Shanghai stock impact on the correlation than the positive shock of the market and EUA market tend to turn even better when same latitude. Meanwhile, the value of g 2 being zero there are increased volatility on the stock market. Therefore, it is concluded that EUA futures are worth to shows that there is no difference between the impacts of be considered by Chinese investors to diversify their the negative shock and positive shock on Shanghai stock investments. market on the correlation. The weak correlation between EUA market and c1 c2 c3 c4 stock market could be explained by the significantly value 0.1911 0.0308 0.0684 0.9315 different market fundamentals. The factors affecting the p-value 0.2032 0.1773 0.0000 0.0000 demand and supply of EUA are very different from the AIC 4.373437 counterparts on financial market. The supply of EUA is SBC 4.406207 determined by the member states of European Union and is certain in a single year. The demand of EUA is Tab. 3: The estimation result of the mean-volatility model of determined by the emissions of the sources covered in Shanghai Composite Index yields the EU ETS, which is further affected by the economic Tab. 4: Coefficient in the dynamic correlation model growth, fuel prices, and weather conditions and so on. Therefore, in terms of price determination, the assets
  6. 6. Accepted by International Conference on Management Science and Engineering, May 2009 6 involving EUA are very different from the financial Sciences in China, 2003 (02):68-73. (in Chinese) assets. As to the trading of EUA futures, according to [5] Bollerslev, T., R. F. Engle, and J. M. Wooldridge. A ECX, the banks have taken the second largest part of the capital-asset pricing model with time-varying covariance traders, only less than the utilities covered in EU ETS. [J]. Journal of Political Economy. 1988(96):116–131. Meanwhile, more and more emerging speculative traders [6] Bollerslev, T.. Modeling the coherence in short run and brokers are being involved in carbon trading. It is nominal exchange rates: A multivariate generalized obvious that, the purpose of trading of EUA futures is ARCH Model [J]. Review of Economics and Statistics, now not limited to that of meeting the commitments in 1990(72): 498–505. emission reduction schemes. More and more trades are [7] Engle R. F, Kroner K F. Multivariate simultaneous aimed to seek the profit brought up the emerging EUA generalized ARCH [J]. Econometric Theory, 1995 futures market. EUA futures have become a new but (11):122—155 important kind of financial asset and will take larger and [8] Engle, R.F.. Dynamic conditional correlation: a larger space on the international financial market. This is simple class of multivariate generalized autoregressive the reason of the paper calling for more attention on the conditional heteroskedasticity models [J]. Journal of new asset. Business and Economics Statistics, 2002 (20):339–350. [9] C. Kearney, V. Pot`ı.. Correlation dynamics in 5 Conclusion European equity markets [J]. Research in International This paper analyzes the dynamic correlation Business and Finance. 2006(20): 305–321 between EUA futures and Shanghai Composite Index [10] Anders C. Johansson.. Interdependencies among using the AGDCC-GARCH model. The analysis on the Asian bond markets [J]. Journal of Asian Economics, EUA futures shows that, the yields of EUA futures 2008(19): 101–116 possess similar characteristics as securities on the capital [11] Liu Guoguang, Zhang Bin. The Correlational market, i.e. “heavy tail” and “volatility clustering”. The analyses of share return and transaction volume based on result of the AGDCC - GARCH model shows that there DCC multivariate CARCH model [J]. Journal of is very weak correlation between the yields of EUA Yancheng Institute of Technology(Natural Science),, futures and Shanghai Composite Index. Moreover, the 2005 (03),19-22.(in Chinese) correlation tend to decrease when the volatility on [12] Zhou Shaopu, Pan La. Correlation of Growth Shanghai stock market increases, further proving that Enterprise Markets in Asian [J]. Statistics and Decision, EUA futures could be used by Chinese investors to 2006 (04),74-77. (in Chinese) diversify their investments on stock market. [13] Gu Yao, Lu Lila. 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  7. 7. Accepted by International Conference on Management Science and Engineering, May 2009 7 Generale des Etudes.