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Study on the wandering weekday effect of the international carbon market based on trend moderation effect
Finance Research Letters 28 (2019) 319–327
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Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Study on the wandering weekday effect of the international carbon market based on trend moderation effect
T
⁎
Chen Zhanga,b,c, Po Yuna,b, , Zulfiqar Ali Wagana,b,d a
Institute of Management Decision and Control, Hefei University of Technology, Hefei, Anhui Province, 230009, China School of Management, Hefei University of Technology, Hefei, Anhui Province, 230009, China Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, Anhui Province, 230009, China d Education and Literacy Department, Govt. of Sindh, Karachi, 74000, Pakistan. b c
A R T IC LE I N F O
ABS TRA CT
Keywords: The international carbon market Wandering weekday effect Trend moderation effect GARCH model
The wandering weekday effect of the international carbon market is a neglected topic. This paper investigates the wandering weekday effect of the international carbon market under the moderation effect of market trend. Our results show that there is a positive wandering Monday and negative wandering Tuesday effect when the market is rising, and a negative wandering Monday and positive wandering Tuesday effect when the market is falling. Further studies find that the settlement procedures, information disclosure and the determinants of carbon prices are stronger reasons of the wandering weekday effect. The conclusion provides new evidence for the study of market-efficiency in international carbon market.
JEL Classification: G13 G14 G15
1. Introduction The international carbon market was formally established in 2005 with an aim to control the global greenhouse gas emissions. As many of countries have begun to pay attention to environmental issues, the international carbon market is developing rapidly. The participants have expanded from the suppliers and demanders of carbon quota to professional investors, including fund companies, commercial banks, investment banks and others. The development of the carbon market makes its price mechanism more mature, however, several studies find that this market still constitutes a nonlinear dynamic system with fractal and non-convergent saturated chaotic characteristics. Moreover, it has spillover relations with other financial markets, which proves that international carbon market is non-effective (Daskalakis & Raphael, 2008; Cao and Xu, 2016; Yang and Liang, 2017). The motivation of this paper is to investigate the existence and explanation of the weekday effect in the international carbon market, which supports another powerful evidence of the research on market efficiency. The fixed weekday effect is an important evidence of the lack of efficiency of the financial market. It means asset returns no longer follow random walk but exhibit periodic volatility and predictability. The most commonly observed pattern is significant negative Monday and positive Friday effect. Baker et al. (2008) suggest that the returns of Canadian stock market have been observed to be the lowest on Monday and the highest on Friday. After an analysis of the weekly bid-ask spread of 734 NASE listed companies, Narayan et al. (2014) suggest the price difference on Friday to be the highest, followed by that on Monday. Based on this trend, Zhang et al. (2017) draw a conclusion that Monday anomalies are seen in the stock market of China, America, Italy, Argentina, and Poland, while Friday anomalies in Brazil, Chile, Turkey, India, Spain and others. However, some other studies maintain that the highest earnings are recorded on Friday, while the lowest returns are not on Monday. Feng (2000) reveal that the stock market of
⁎
Corresponding author. Hefei University of Technology, No. 193 Tunxi Road, BaoHe District, Hefei, Anhui, China, 230009. E-mail addresses: [email protected] (C. Zhang), [email protected] (P. Yun).
https://doi.org/10.1016/j.frl.2018.05.014 Received 21 December 2017; Received in revised form 23 May 2018; Accepted 30 May 2018
Available online 18 June 2018 1544-6123/ © 2018 Elsevier Inc. All rights reserved.
Finance Research Letters 28 (2019) 319–327
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Shanghai has a positive Friday and negative Tuesday effect. Chiaku and Mete (2008) propose that the lowest returns are observed on Monday in the 5-day trading system of the stock market, whereas in the 6-day trading system, the lowest returns are on Tuesday. However, the assumption of the fixed weekday effect is that seasonal anomaly should become steady over time, rather than a continual state of flux, which may be difficult to grasp the changing characteristics of returns. As a contrast, the wandering weekday effect is another evidence of the non-efficiency of the financial market, which assumes the pattern of daily seasonality may shift over time, yet in a manner that is distinguishable from a random process. Jaffe et al. (1989) suggest that financial market undergoes a negative twist Monday effect, which improves significantly when market is in down-trend and disappears in up-trend. However, Doyle and Chen (2009) insist that the wandering weekday effect is sustainable and has no significant correlation with previous returns. Referring to Doyle's research, Boubaker et al. (2017) examine the sensitivity of the wandering weekday effect with respect to the error distributions, the results show that this sensitivity is found in about 82% (42 out of 51) of all indices. The international carbon market defines the permission of carbon emissions as valuable assets, the operating mechanism and trading regulation are significantly different from other financial markets, which may contribute to different patterns and explanations of the weekday effect. Therefore, it is necessary to understand the existence of the wandering weekday effect in the international carbon market and its reasons, which form the purpose of this paper. To achieve the above goals, this paper investigates the following innovations: First, the returns of carbon market are divided into two states: high-frequency volatility state and low-frequency volatility state. Each state manifests two prominent market trends: rising trend and falling trend; second, we take the market trend as a moderator to measure the wandering weekday effect under different frequency volatility and tail distribution; third, we support stronger explanations of the wandering weekday effect from the settlement procedures, information disclosure and the determinants of carbon prices. The layout of this article is as follows: Section 2 introduces the research design. Section 3 presents the empirical results of the fixed and the wandering weekday effect and analyzes its reasons. Section 4 constitutes the conclusion. 2. Research design 2.1. The identification of the frequency volatility state and market trends The European Union's Emissions Trading System (EU ETS) is the largest carbon market in the world. Among many of the trading products in this market, the European Union Allowance (EUA) futures, especially, have long trading history and are large in proportion and volume. Moreover, the price discovery mechanism is better than that of other products. So, we choose EUA futures to study the wandering weekday effect of the international carbon market. The sample period is from January 12, 2009 to July 28, 2017, and the returns take the natural logarithm of the price sequence.
Rt = 100 × (lnPt − lnPt − 1)
(1)
where Pt,Pt − 1 denotes the carbon price at time t and t-1 respectively, Rt indicates the returns. Fig. 1 shows the volatility of the international carbon return. For reflecting the volatility of returns accurately, this paper divides the carbon returns into two states: high-frequency volatility and low-frequency volatility (as in Eq. (2)). The volatility in highfrequency volatility and low-frequency volatility state is shown in Fig. 2.
Fig. 1. The volatility of the international carbon returns in 2009.1.13–2017.7.28. 320
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Fig. 2. Volatility of the international carbon returns in high-frequency and low-frequency volatility state. n
Rt =
⎧ high − frequency volatility state Rt , if Rt − R ≥ ∑t = 1 Rt − R /n ⎨ low − frequency volatility state Rt , if Rt − R < ∑tn= 1 Rt − R /n ⎩
(2)
n ∑t = 1
where R means the average returns of carbon price; Rt − R / n represents the square difference of returns volatility. The investors' attitudes and psychology to risk can depart significantly from the predictions of expected utility according to the prospect theory. Specifically, the investors are assumed to derive utility from gains and losses, the individual forms a mental representation of the gains and losses he associates with taking the risk, and then the individual evaluates this representation –this distribution of gains and losses–to see if it is appealing (Tversky and Kahneman, 1992). Based on the analysis, we divide the market trend of carbon returns into rising and falling trend and studied the daily trading decisions driven by the investors' attitudes and psychology. Inspired by Varma (2005), we divide the market trend into rising and falling trend (as in Eq. (3)).
TR, j = 1(Tup = Pt − Pt − 1, if Pt − Pt − 1> 0 and 0 otherwise) Trendj = ⎧ ⎨ ⎩TF , j = 2(Tdown = Pt − Pt − 1, if Pt − Pt − 1< 0 and 0 otherwise)
(3)
where TR and TF represents the rising and falling trend. In high-frequency volatility state, the returns of the rising and falling trend shown in Fig. 3 range from 0 to 2 and −1.6 to 0 respectively; in low-frequency volatility state, however, the returns shown in Fig. 4 range from 0 to 0.4 and −0.4 to 0 respectively, which manifests less volatility than that in high-frequency volatility state. 2.2. The identification model of the weekday effect Consider the heteroscedasticity of the carbon returns, this paper conducts the generalized autoregressive conditional heteroskedasticity (GARCH) model to measure the wandering weekday effect. We add the first order lag of returns into the regression equation to overcome the self-correlation of the carbon returns sequence.
Rt = Rt − 1 +
5
∑i =1 φi Dit + ɛ1t
i = 1, 2, 4, 5
(4)
where Rt,Rt-1 denotes the international carbon returns and the first order lag of returns. To avoid the virtual trap, this paper assumes Wednesday as a benchmark to measure only the returns volatility on Monday, Tuesday, Thursday, and Friday, i = 1, 2, 4, 5, and Dit represents daily dummy variable, if i = 1, means the trading day is Monday and D1t=1;D1t=0 otherwise. Other dummy variables are defined similarly. The fixed weekday effect does not include the moderation effect of market trends, AR (1)-GARCH (1,1) model is used to check the fixed weekday effect. The model is expressed as follows:
Rt = α 0 + α1 Rt − 1 +
5
∑i =1 φi Dit + ɛ3t
(5) 321
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Fig. 3. Volatility of the international carbon returns under the rising and falling trend in high-frequency volatility state.
Fig. 4. Volatility of the international carbon returns under the rising and falling trend in low-frequency volatility state. 2 2 σt2 = α 0 + α1 ɛ3, t − 1 + β1 σt − 1
(6)
To reflect the wandering weekday effect and capture the changing characteristics of carbon returns depicted in Fig. 3 and Fig. 4, we take the market trend as a moderator in the mean equation of the GARCH (1, 1) model. We identify the patterns of the wandering weekday effect by analyzing the cross-multiplication term of daily dummy variables and market trends. The model is T-AR (1)322
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Table 1 Descriptive statistics. Panel A: 2009.1.13–2017.7.28
Mean
Std. Dev
Skewness
Kurtosis
J-Bera
Prob
Monday Tuesday Wednesday Thursday Friday
−0.231 −0.018 0.112 −0.004 −0.112
2.876 3.217 2.806 2.862 3.197
1.844 −1.922 −0.24 −1.382 1.563
21.147 34.35 8.785 16.765 25.135
6058.36 18,289.57 617.873 3605.493 8953.538
0.000 0.000 0.000 0.000 0.000
Panel B: high-frequency volatility state
Mean
Std.Dev
Skewness
Kurtosis
J-Bera
Prob
Monday Tuesday Wednesday Thursday Friday
−0.441 −0.056 0.322 0.094 −0.169
4.542 5.28 4.586 4.773 5.365
1.418 −1.231 −0.291 −0.969 0.943
9.616 13.569 3.65 6.691 9.482
334.7 745.816 4.795 104.993 273.387
0.000 0.000 0.091 0.000 0.000
Panel C: low-frequency volatility state
Mean
Std.Dev
Skewness
Kurtosis
J-Bera
Prob
Monday Tuesday Wednesday Thursday Friday
−0.119 0.002 0.002 −0.052 −0.159
1.069 1.023 1.005 1.02 0.969
0.057 −0.061 −0.04 0.099 0.087
1.881 2.093 1.955 2.037 2.169
14.117 10.053 13.234 11.837 8.593
0.001 0.007 0.001 0.003 0.014
GARCH (1,1) and expressed as follows: 5
Rt = α 0 + α1 Rt − 1 +
2
5
2
∑ φi Dit + ∑ δj Trendjt + ∑ ∑ θij Trendj × Di + ɛ4t i=1
j=1 5
σt2 = α 0 + α1 ɛ24, t − 1 + β1 σt2− 1 +
i=1 j=1 2
5
2
∑ φi Dit + ∑ δj Trendjt + ∑ ∑ θij Trendj × Di i=1
j=1
(7)
i=1 j=1
(8)
where Dit and Trendj × Di represent daily returns and daily returns under the moderation effect of market trend respectively. For depicting the influence of market volatility, the variance is introduced into the mean equation of above models, and the referring model of AR (1)-GARCH (1,1)-M and T-AR (1)-GARCH (1,1)-M is obtained. To reflect the sensitivity of tail distribution to the wandering weekday effect, this article also conducts the empirical model under t and GED distribution respectively. Moreover, the AIC principle is used to determine the optimal distribution model. The smaller the AIC value, the better the model in reflecting the tail returns. 3. Empirical analysis 3.1. Descriptive statistics analysis The descriptive statistics of the sample are show in Table 1. For total sample and high-frequency volatility state, the highest average returns are on Wednesday, and the earnings on Monday are said to be the lowest. There is a significant peak fat-tailed phenomenon in all trading days, which indicates that the international carbon market does not conform to the laws of normal distribution. For low-frequency volatility state, the highest returns are observed on Tuesday and Wednesday, while the lowest are seen on Friday, the skewness is around 0 and the kurtosis is less than 3, those results show that the market is basically consistent with the normal distribution in low-frequency volatility state. 3.2. Analyzing the fixed weekday effect Empirical results recorded in Table 2 show that in high-frequency volatility state, there is a negative fixed Monday effect under the t and GED distribution. Additionally, the model AR (1)-GARCH (1,1)-M displays a better fitting performance according to the AIC minimum principle. However, when market in low-frequency volatility state, as shown in Table 3, the AR (1) -GARCH (1,1) model reflects a negative Friday effect under the t distribution, while under the GED distribution exhibits a negative Monday effect. Moreover, the fixed Monday effect under the GED distribution is shown to be more effective in depicting tail returns. Low-frequency volatility means lower risk of the returns, indicates no significant difference among daily returns, which reduces the impact of risk on daily earnings. Therefore, we can conclude that there is a significant negative fixed Monday effect in the international carbon market. However, the assumption behind the fixed weekday effect insist seasonal anomaly should become steady, that means the volatility of the returns of international carbon market is stable over time, which is contrary to the changing characteristics of returns depicted in Fig. 1 and Fig. 2, let alone reflect the return volatility under different market trends accurately. To overcome those defects, a 323
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Table 2 Testing the fixed weekday effect in high-frequency volatility state of the international carbon market. AR(1)-GARCH(1,1)
AR(1)-GARCH(1,1)-M
Coff-t
Coff-GED
Mean D1 D2 D4 D5 AIC R2
−0.935 −0.330 −0.205 −0.551 5.8479 0.0049
Vari ⁎⁎
0.132 3.449 2.383 0.941
Mean −0.818 −0.427 −0.194 −0.537 5.8633 0.0006
Coff-t Vari
⁎⁎
0.622 6.670* 5.667* 1.686
Coff-GED
Mean −0.956 −0.296 −0.182 −0.552 5.8441 0.004
⁎⁎
Vari
Mean
Vari
0.040 3.281 2.224 0.886
−0.817* −0.389 −0.158 −0.528 5.8658 0.0056
0.507 6.431 5.606* 1.640
Notes: The result is calculated according to the Eqs. (5) and (6). *, **, *** denote the statistical significance at 10%, 5%, and 1%. Table 3 Testing the fixed weekday effect in low-frequency volatility state of the international carbon market. AR(1)-GARCH(1,1)
AR(1)-GARCH(1,1)-M
Coff-t Mean D1 D2 D4 D5 AIC R2
−0.096 0.023 −0.034 −0.152* 2.8789 0.0094
Coff-GED Vari 0.133 0.030 0.031 −0.106
Mean −0.046 −0.024 −0.008 0.002 2.7135 0.0009
⁎⁎
Coff-t
Coff-GED
Vari
Mean
Vari
Mean
Vari
−0.037 0.013 0.010 −0.003
−0.031 0.031 −0.016 −0.197 2.8798 0.0099
0.134 0.017 0.025 −0.102
−0.065 −0.018 0.017 −0.088 2.7267 0.0059
−0.021 −0.018 −0.005 −0.006
Notes: The result is calculated according to the Eqs. (5) and (6). *, **, *** denote the statistical significance at 10% , 5% and 1%.
wandering weekday effect with the moderation of market trends under high and low frequency volatility state is tested. 3.3. Analyzing the wandering weekday effect 3.3.1. Analyzing the pattern of the wandering weekday effect By empirical analysis, we conclude that under the t distribution, when the market in high-frequency volatility state, as depicted in Table 4, there is a negative Monday and positive Tuesday effect. However, under the moderation of market trends, there is a positive wandering Monday and negative wandering Tuesday effect when the market rises, while manifests a negative wandering Monday and Table 4 Testing the wandering weekday effect in high-frequency volatility state of the international carbon market based on trend moderation effect. T-AR(1)-GARCH(1,1) Coff-t
D1 D2 D4 D5 TR TF TR*D1 TR*D2 TR*D4 TR*D5 TF*D1 TF*D2 TF*D4 TF*D5 AIC R2
T-AR(1)-GARCH(1,1)-M Coff-GED
Coff-t
Coff-GED
Mean
Vari
Mean
Vari
Mean
Vari
Mean
Vari
−1.362⁎⁎⁎ 0.828⁎⁎ 0.041 −0.653 10.579⁎⁎⁎ 11.906⁎⁎⁎ 3.601⁎⁎⁎ −2.838⁎⁎⁎ 0.531 4.044⁎⁎⁎ −4.168⁎⁎⁎ 3.682⁎⁎⁎ 0.342 0.388 4.0838 0.8215
−1.348 −3.699* −1.172 −3.337 −0.838 0.453 5.811 1.554 −4.221 −0.444 3.971 −6.845 −2.728 −0.395
−1.361 0.961 0.019 −0.711 10.618⁎⁎⁎ 11.888⁎⁎⁎ 3.474* −2.811* 0.567 4.599⁎⁎ −4.23⁎⁎ 4.169⁎⁎ 0.292 0.328 4.3726 0.8218
−1.195 −1.005 −0.781 −1.372 −0.882 0.300 −0.265 −0.890 −4.890 −1.500 4.435 0.078 −0.117 1.873
−0.933⁎⁎ 0.806⁎⁎ 0.170 0.160 11.863⁎⁎⁎ 13.051⁎⁎⁎ 4.442⁎⁎⁎ −1.040⁎⁎ 2.099* 1.848* −3.311⁎⁎⁎ 3.242⁎⁎⁎ 0.477 1.261 3.6951 0.7942
−2.464 −3.796* −3.630* −3.679* −0.073 0.562 0.195 1.685 1.850 0.580 2.672 −2.298 −1.004 −1.381
−1.032* 0.840 0.248 0.180 11.723⁎⁎⁎ 13.174⁎⁎⁎ 4.534⁎⁎⁎ −1.350 1.719 2.005 −3.528⁎⁎ 3.735⁎⁎ 1.246 1.997 3.7811 0.8007
−2.704 −3.588⁎⁎ −3.122* −3.693⁎⁎ −0.103 −0.393 0.012 0.844 −1.003 1.236 3.085 −2.051 −2.943 −0.771
Notes: The result is calculated by the Eqs. (7) and (8). *,⁎⁎,⁎⁎⁎denote the statistical significance at 10%, 5% and 1%. 324
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Table 5 Testing the wandering weekday effect in low-frequency volatility state of the international carbon market based on trend moderation effect. T-AR(1)-GARCH(1,1) Coff-t Mean D1 D2 D4 D5 TR TF TR*D1 TR*D2 TR*D4 TR*D5 TF*D1 TF*D2 TF*D4 TF*D5 AIC R2
0.011 0.048 −0.008 −0.013 7.781⁎⁎⁎ 6.996⁎⁎⁎ −0.921 −0.440 −0.620 −1.185 0.429 0.603 −0.426 −0.269 1.1091 0.7974
T-AR(1)-GARCH(1,1)-M Coff-GED
Vari −0.097* −0.086 −0.089* −0.070 −0.137 0.130 −0.156 −0.162 −0.304 −0.311 0.047 0.060 0.352 0.314
Mean 0.056 0.070 −0.017 −0.029 8.299⁎⁎⁎ 7.029⁎⁎⁎ −1.840⁎⁎⁎ −0.719 −0.432 −1.356⁎⁎ 0.628 1.418⁎⁎ −0.723 −0.411 1.1514 0.8012
Coff-t Vari
Mean
−0.067 −0.193⁎⁎⁎ −0.074 −0.061 0.145 0.126 −0.455⁎⁎⁎ 0.261 −0.517⁎⁎⁎ −0.560⁎⁎⁎ 0.188 −0.814* 0.396 0.335
0.005 −0.012 −0.022 −0.021 7.277⁎⁎⁎ 7.066⁎⁎⁎ −1.402⁎⁎ −0.683 −0.723 −1.260* 0.338 −0.006 −0.182 0.076 1.0484 0.7892
Coff-GED Vari ⁎⁎
−0.104 −0.144⁎⁎⁎ −0.082⁎⁎ −0.063 −0.117 0.144 −0.227 0.036 −0.299 −0.331 0.125 −0.076 0.320 0.339
Mean
Vari
−0.006 −0.039 −0.012 −0.009 7.183⁎⁎ 6.740⁎⁎ −1.254⁎⁎⁎ −0.714* −0.752⁎⁎ −1.115⁎⁎⁎ 0.299 −0.150 −0.198 −0.003 0.9977 0.7803
−0.097 −0.141⁎⁎ −0.082 −0.058 −0.141 0.151 −0.183 0.007 −0.276 −0.352 0.173 0.008 0.328 0.380
Notes: The result is calculated by the Eqs. (7) and (8). *,⁎⁎,⁎⁎⁎denote the statistical significance at 10%, 5% and 1%.
positive wandering Tuesday effect when the market falls. Under the GED distribution, the model T-AR(1)-GARCH(1,1) does not present any pattern of wandering weekday effect, while the T-AR(1)-GARCH(1,1)-M model displays a negative Monday effect and reverses to a positive wandering Monday effect when the market rises and remains a negative one when the market falls. Different models depict different patterns of wandering weekday effect under different distributions, while the T-AR(1)-GARCH(1,1)-M model is more effective under the t distribution based on the AIC principle. When the market in low-frequency volatility state, as in Table 5, the result suggests that there is no wandering weekday effect. Therefore, we conclude that the international carbon market has a positive wandering Monday and negative wandering Tuesday effect when the market rises and a negative wandering Monday and positive wandering Tuesday effect when market falls. 3.3.2. Comparing the performance of model between fixed and wandering weekday effect AIC is a standard to measure the performance of the statistical model. Furthermore, we find that the AIC value of wandering weekday effect in high and low frequency volatility state, which show in Table 4 and Table 5 are smaller than that of fixed weekday effect in Table 2 and Table 3. This conclusion also supports the claim that the wandering weekday effect is more accurate and reliable to describe daily volatility than fixed weekday effect, which is in line with the study conducted by Doyle and Chen (2009) and Boubaker et al. (2017). 3.4. Discussing the reasons of wandering weekday effect 3.4.1. Reasons from the settlement procedures and information disclosure system The settlement procedures and information disclosure system are popular reasons for the weekday effect of financial markets (Patel and Mallikarjun, 2014; Zhang et al., 2015). Frist, the settlement procedures followed in the international carbon market regulates that the carbon products delivery takes place 3 days after the last trading day according to the Intercontinental Exchange (ICE), which encourages frequent trading on Monday and Tuesday for reducing the opportunity cost and risk of futures holding, makes the gains of those two days significantly different from other trading days. Second, the information disclosure system according to the ICE rules that the trading suspension within weekend makes the gains of the following Monday and Tuesday contain more trading information and uncertainty than other days, increases price volatility, thereby making it easy to increase the motivation of speculation and trading on those days. This explanation has been convinced as a common reason of the weekday effect in other financial markets, including the carbon markets, which trading suspension within weekend (Zhang et al., 2015). Driven by those two reasons, investors' psychology and the resulting trading decisions usually show great difference under different volatility state and market trends. In high-frequency volatility state, when market is rising, the corresponding expected return is higher and investor confidence rises, the carbon market investors tend to increase their Monday's holdings, which results a substantial increase in earnings on Monday. However, high-frequency fluctuating characteristics of the market means the wandering Monday effect is usually not sustainable, investors will take risk hedging transactions and dispose carbon assets timely for risk aversion on Tuesday, resulting in a sharp decline of Tuesday's earnings, which form a negative wandering Tuesday effect. While when market is falling, the market prospect is not optimistic, the carbon market investors tend to take short sell deals and reduce the holding of carbon asset on Monday, which results a short decline of Monday's earnings. Driven by excess returns, however, investors are more likely to take reverse operations and prone to increase their Tuesday's holdings, which results a big boost of Tuesday's 325
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Table 6 Analyzing the determinants of the wandering Monday and Tuesday effect under the rising and falling trend of the carbon market.1 Rising-trend
wandering weekend effect Rt( − 20) Rt( − 120) Coal Power Oil Gas Macro R2
Falling-trend
Monday
Tuesday
Monday
Tuesday
4.442⁎⁎⁎ 0.0012 0.0172* 0.0031 0.0034 −0.0037 −0.0006 −0.0092 0.0939
−1.040⁎⁎ 0.0575⁎⁎ −0.0393 0.0344 −0.1998⁎⁎ −0.1114⁎⁎ −0.0964* 0.3997⁎⁎⁎ 0.0369
−3.311⁎⁎⁎ −0.0091⁎⁎⁎ −0.0105⁎⁎⁎ 0.0076 −0.0167 −0.0101 0.0016 0.0207 0.2465
3.242⁎⁎⁎ −0.0423⁎⁎⁎ −0.0132 0.0199 −0.1358 −0.0336 0.0422 0.2035 0.105
Notes: The result is calculated by the Eqs. (9) and (10). *,⁎⁎,⁎⁎⁎denote the statistical significance at 10%, 5% and 1%.
returns. In low-frequency volatility state, however, the return volatility is low, the market risk is controllable or affordable, and investors are prone to adopt long-term and stable investment strategies. Therefore, irrespective of whether the market is rising or falling, there is little change in daily returns and does not exhibit any patterns of wandering week effect. 3.4.2. Reasons from the determinants of carbon prices Plenty of researches have been convinced that the returns of international carbon market are closely related to the returns of energy market and macroeconomy (Byun and Cho, 2013; Zhang and Yang, 2016). As complementary investment products, carbon returns are negatively correlated with other energy returns. The macroeconomy usually show positively relationship with the energy consumption and carbon prices. Based on this, this paper selects the prices of coal, electricity, oil and natural gas, which are consumed in large amounts of the international energy market, and macroeconomic indicators to detect the determinants of the wandering Monday and Tuesday effect. The model is GARCH (1,1) and expressed as follows:
Di × Rt = γ1 Rt (−20) + γ2 Rt (−120) + γ3 Coal + γ4 Power + γ5 Oil + γ6 Gas + γ7 Marco + ɛ5t σt2
= α0 +
α1 ɛ5,2 t − 1
+
β1 σt2− 1
+ η1 Coal + η2 Power + η3 Oil + η4 Gas + η5 Marco
(9) (10)
Where Di × Rtrepresent the wandering weekday effect recognized by the Eqs. (7) and (8). Coal and Power are assumed to be Australia BJ coal spot prices and Basic European power index; Oil is replaced by Brent crude oil futures prices; Gas prices from the UK natural gas continuous futures prices; The European Stoxx 50 (Macro) is selected to indicate the macroeconomy. The returns adhere to the natural logarithm of price sequence. Furthermore,Rt( − 20)andRt( − 120) are replaced by the long and short terms of the returns from the past 1 and 6 months respectively. The results show (see Table 6) that when market is rising, the wandering Monday effect is influenced significantly by the longterm returns, while the wandering Tuesday effect is affected by the short-term returns. The historical returns of the carbon market are the most valuable reference for investors to make trading decisions on Monday. As a result, investors tend to continue the long-term trading strategies adopted on Mondays in the past, thereby the earnings of Monday positively related to the long-term earnings. While for Tuesday, investors can refer to Monday's trading decisions and other energy market information, so that the Tuesday's earnings are greatly influenced by short-term returns. Further research shows that the Tuesday's returns are also negatively related to electricity, oil and gas returns and positively related to the macroeconomy. When the market in high-frequency volatility state, the shortterm investors tend to adopt reverse arbitrage trading on Tuesdays after increasing the holdings on Monday. Therefore, as complementary investment products, the returns of electricity, oil, and gas on Tuesdays are negatively related to the carbon returns. For macroeconomic indicators, the better is the economic prospect, the faster the growth of the entity businesses and the carbon emissions will further promote the rise of the carbon prices. When the market is falling, however, the wandering Monday effect is only negatively affected by its long and short trend, while the wandering Tuesday effect is affected by its short trend and macroeconomy. Other energy prices and macroeconomic factors have little reference for investors' decision-making on Mondays when the carbon market depicts a falling trend. In fact, a brief decline in Monday's returns also provide a certain profit space for arbitrage and hedging transactions on Tuesdays. As a result, investors will increase their holding of carbon futures contracts on Tuesday driven by profit-seeking psychology in the short term. 4. Conclusions This paper focuses on the study of the wandering weekday effect of the international carbon market based on the perspective of market inefficiency, which overcome the defects of fixed weekday effect that seasonal anomaly should become steady over time. The results show that the international carbon market manifests a wandering weekday effect only in high-frequency volatility state, there 1 The data of Coal and Oil originate from the Wind database; Gas data from the ICE; Power data from the European electric power Exchange(EEX); Macro data from STOXX. The period is from January 12, 2009 to July 28, 2017.
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is a positive wandering Monday and negative wandering Tuesday effect when market is rising, and a negative wandering Monday and positive wandering Tuesday effect when market is falling. Further analysis shows that the settlement procedures, information disclosure system and the determinants of carbon returns, especially its long and short-trend and macroeconomy are stronger reasons for the wandering Mondays and Tuesdays effect. In research, we also confirm that the wandering weekday effect observed in the international carbon market is not robust to the choice of error distribution, which is supported by Boubaker et al. (2017) conclusions about the weekday effect with respect to the stock market. The study of the wandering weekday effect under the moderation of rising and falling trends in high and low frequency state is more reasonable and accurate to detect the volitionally of daily returns of the international carbon market. The patterns of wandering weekday effect encourage investors to take risk hedging and arbitrage trade driving by investors' attitudes and psychology to risk according to the prospect theory. As the improvement of the diversification of carbon investors, the profit space will be compressed, the carbon market will gradually return to the state of equilibrium, and then market efficiency will be promoted. To conclude, the findings of this article provide a new evidence against the Efficient Market Hypothesis and contribute to the decision-making and improvement of market efficiency in the international carbon market. Acknowledgment The authors thank the National Natural Science Foundation of China under Grant [71373065] for supporting this research work. Conflicts of interest None. References Baker, H.K., Rahman, A., Saudi, S., 2008. The day-of-the-week effect and conditional volatility: sensitivity of error distributional assumptions. Rev. Financ. Econ. 17, 280–295. https://doi.org/10.1016/j.rfe.2007.09.003. Boubaker, S., Essaddam, N., Nguyen, D.K., Saadi, S., 2017. On the robustness of week-day effect to error distributional assumption: international evidence. J. Int. Financ. Mark. Inst. Money. 47, 114–130. https://doi.org/10.1016/j.intfin.2016.11.003. Byun, S.J., Cho, H., 2013. Forecasting carbon futures volatility using GARCH models with energy volatilities. Energy Econom. 2, 207–221. https://doi.org/10.1016/j. eneco.2013.06.017. Cao, G., Xu, W., 2016. Multifractal features of EUA and CER futures markets by using multifractal detrended fluctuation analysis based on empirical model decomposition. Chaos Solitons Fractals 83, 212–222. https://doi.org/10.1016/j.chaos.2015.12.010. Chiaku, C., Mete, F., 2008. An econometric investigation of the day-of-the-week effect and returns volatility in Fifteen Asia Pacific Financial Markets (1998-2003). Appl. Econom. Int. Dev. 6, 207–220. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1240722. Daskalakis, G., Raphael, N.M., 2008. Are the European carbon markets efficient? Rev. Futures Mark. 17, 103–128. http://ssrn.com/abstract=1003989. Doyle, J.R., Chen, C.H., 2009. The wandering weekday effect in major stock markets. J. Bank Financ. 33, 1388–1399. https://doi.org/10.1016/j.jbankfin.2009.02.002. Feng, L.C., 2000. The week effect in Chinese stock market. Econ. Res. 9, 50–57. Jaffe, J.F., Westerfield, R., Ma, C., 1989. A twist on the Monday effect in stock prices: evidence from the US and foreign stock markets. J. Bank Financ. 13, 641–650. https://doi.org/10.1016/0378-4266(89)90035-6. Narayan, P.K., Mishra, S., Narayan, S., 2014. Spread determinants and the day-of-the-week effect. Q. Rev. Econ. Financ. 54, 51–60. https://doi.org/10.1016/j.qref. 2013.07.008. Patel, S.A., Mallikarjun, M., 2014. Settlement cycle and day of the week anomaly: empirical evidence from Indian stock market. Decis 41, 327–337. https://doi.org/10. 1007/s40622-014-0050-4. Tversky, A., Kahneman, D., 1992. Advances in prospect theory: cumulative representation of uncertainty. J. Risk. Uncertainty 5, 297–323. http://media.longnow.org/ files/2/REVIVE/Advances%20in%20prospect%20theory.pdf. Verma, R., Verma, P., 2005. Do emerging equity markets respond symmetrically to US market upturns and downturns? Evidence from Latin America. Int. J. Bus. Econ. 4, 193–208. http://www.ijbe.org/table%20of%20content/pdf/vol4-3/vol4-3-02.pdf. Yang, X., Liang, J.L., 2017. Analysis and test of fractal and chaotic behavior characteristics of the international carbon emissions market. Syst. Eng. -Theory Pract. 37, 1420–1431. http://www.sysengi.com/EN/Y2017/V37/I6/1420. Zhang, C., Yang, X.Z., 2016. Forecasting of China's regional carbon market price based on multi-frequency combined model. Syst. Eng. -Theory Pract. 36, 3017–3025. http://www.sysengi.com/CN/abstract/abstract111445.shtml. Zhang, J., Lai, Y., Lin, J., 2017. The day-of-the-week effects of stock markets in different countries. Financ. Res. Lett. 20, 47–62. https://doi.org/10.1016/j.frl.2016.09. 006. Zhang, T.W., Chueh, H., Yao, H.H., 2015. Day-of-the-week trading patterns of informed and uninformed traders in Taiwan's foreign exchange market. Econ. Model. 47, 271–279. https://doi.org/10.1016/j.econmod.2015.03.004.
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Study on the wandering weekday effect of the international carbon market based on trend moderation effect
T
⁎
Chen Zhanga,b,c, Po Yuna,b, , Zulfiqar Ali Wagana,b,d a
Institute of Management Decision and Control, Hefei University of Technology, Hefei, Anhui Province, 230009, China School of Management, Hefei University of Technology, Hefei, Anhui Province, 230009, China Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, Anhui Province, 230009, China d Education and Literacy Department, Govt. of Sindh, Karachi, 74000, Pakistan. b c
A R T IC LE I N F O
ABS TRA CT
Keywords: The international carbon market Wandering weekday effect Trend moderation effect GARCH model
The wandering weekday effect of the international carbon market is a neglected topic. This paper investigates the wandering weekday effect of the international carbon market under the moderation effect of market trend. Our results show that there is a positive wandering Monday and negative wandering Tuesday effect when the market is rising, and a negative wandering Monday and positive wandering Tuesday effect when the market is falling. Further studies find that the settlement procedures, information disclosure and the determinants of carbon prices are stronger reasons of the wandering weekday effect. The conclusion provides new evidence for the study of market-efficiency in international carbon market.
JEL Classification: G13 G14 G15
1. Introduction The international carbon market was formally established in 2005 with an aim to control the global greenhouse gas emissions. As many of countries have begun to pay attention to environmental issues, the international carbon market is developing rapidly. The participants have expanded from the suppliers and demanders of carbon quota to professional investors, including fund companies, commercial banks, investment banks and others. The development of the carbon market makes its price mechanism more mature, however, several studies find that this market still constitutes a nonlinear dynamic system with fractal and non-convergent saturated chaotic characteristics. Moreover, it has spillover relations with other financial markets, which proves that international carbon market is non-effective (Daskalakis & Raphael, 2008; Cao and Xu, 2016; Yang and Liang, 2017). The motivation of this paper is to investigate the existence and explanation of the weekday effect in the international carbon market, which supports another powerful evidence of the research on market efficiency. The fixed weekday effect is an important evidence of the lack of efficiency of the financial market. It means asset returns no longer follow random walk but exhibit periodic volatility and predictability. The most commonly observed pattern is significant negative Monday and positive Friday effect. Baker et al. (2008) suggest that the returns of Canadian stock market have been observed to be the lowest on Monday and the highest on Friday. After an analysis of the weekly bid-ask spread of 734 NASE listed companies, Narayan et al. (2014) suggest the price difference on Friday to be the highest, followed by that on Monday. Based on this trend, Zhang et al. (2017) draw a conclusion that Monday anomalies are seen in the stock market of China, America, Italy, Argentina, and Poland, while Friday anomalies in Brazil, Chile, Turkey, India, Spain and others. However, some other studies maintain that the highest earnings are recorded on Friday, while the lowest returns are not on Monday. Feng (2000) reveal that the stock market of
⁎
Corresponding author. Hefei University of Technology, No. 193 Tunxi Road, BaoHe District, Hefei, Anhui, China, 230009. E-mail addresses: [email protected] (C. Zhang), [email protected] (P. Yun).
https://doi.org/10.1016/j.frl.2018.05.014 Received 21 December 2017; Received in revised form 23 May 2018; Accepted 30 May 2018
Available online 18 June 2018 1544-6123/ © 2018 Elsevier Inc. All rights reserved.
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Shanghai has a positive Friday and negative Tuesday effect. Chiaku and Mete (2008) propose that the lowest returns are observed on Monday in the 5-day trading system of the stock market, whereas in the 6-day trading system, the lowest returns are on Tuesday. However, the assumption of the fixed weekday effect is that seasonal anomaly should become steady over time, rather than a continual state of flux, which may be difficult to grasp the changing characteristics of returns. As a contrast, the wandering weekday effect is another evidence of the non-efficiency of the financial market, which assumes the pattern of daily seasonality may shift over time, yet in a manner that is distinguishable from a random process. Jaffe et al. (1989) suggest that financial market undergoes a negative twist Monday effect, which improves significantly when market is in down-trend and disappears in up-trend. However, Doyle and Chen (2009) insist that the wandering weekday effect is sustainable and has no significant correlation with previous returns. Referring to Doyle's research, Boubaker et al. (2017) examine the sensitivity of the wandering weekday effect with respect to the error distributions, the results show that this sensitivity is found in about 82% (42 out of 51) of all indices. The international carbon market defines the permission of carbon emissions as valuable assets, the operating mechanism and trading regulation are significantly different from other financial markets, which may contribute to different patterns and explanations of the weekday effect. Therefore, it is necessary to understand the existence of the wandering weekday effect in the international carbon market and its reasons, which form the purpose of this paper. To achieve the above goals, this paper investigates the following innovations: First, the returns of carbon market are divided into two states: high-frequency volatility state and low-frequency volatility state. Each state manifests two prominent market trends: rising trend and falling trend; second, we take the market trend as a moderator to measure the wandering weekday effect under different frequency volatility and tail distribution; third, we support stronger explanations of the wandering weekday effect from the settlement procedures, information disclosure and the determinants of carbon prices. The layout of this article is as follows: Section 2 introduces the research design. Section 3 presents the empirical results of the fixed and the wandering weekday effect and analyzes its reasons. Section 4 constitutes the conclusion. 2. Research design 2.1. The identification of the frequency volatility state and market trends The European Union's Emissions Trading System (EU ETS) is the largest carbon market in the world. Among many of the trading products in this market, the European Union Allowance (EUA) futures, especially, have long trading history and are large in proportion and volume. Moreover, the price discovery mechanism is better than that of other products. So, we choose EUA futures to study the wandering weekday effect of the international carbon market. The sample period is from January 12, 2009 to July 28, 2017, and the returns take the natural logarithm of the price sequence.
Rt = 100 × (lnPt − lnPt − 1)
(1)
where Pt,Pt − 1 denotes the carbon price at time t and t-1 respectively, Rt indicates the returns. Fig. 1 shows the volatility of the international carbon return. For reflecting the volatility of returns accurately, this paper divides the carbon returns into two states: high-frequency volatility and low-frequency volatility (as in Eq. (2)). The volatility in highfrequency volatility and low-frequency volatility state is shown in Fig. 2.
Fig. 1. The volatility of the international carbon returns in 2009.1.13–2017.7.28. 320
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Fig. 2. Volatility of the international carbon returns in high-frequency and low-frequency volatility state. n
Rt =
⎧ high − frequency volatility state Rt , if Rt − R ≥ ∑t = 1 Rt − R /n ⎨ low − frequency volatility state Rt , if Rt − R < ∑tn= 1 Rt − R /n ⎩
(2)
n ∑t = 1
where R means the average returns of carbon price; Rt − R / n represents the square difference of returns volatility. The investors' attitudes and psychology to risk can depart significantly from the predictions of expected utility according to the prospect theory. Specifically, the investors are assumed to derive utility from gains and losses, the individual forms a mental representation of the gains and losses he associates with taking the risk, and then the individual evaluates this representation –this distribution of gains and losses–to see if it is appealing (Tversky and Kahneman, 1992). Based on the analysis, we divide the market trend of carbon returns into rising and falling trend and studied the daily trading decisions driven by the investors' attitudes and psychology. Inspired by Varma (2005), we divide the market trend into rising and falling trend (as in Eq. (3)).
TR, j = 1(Tup = Pt − Pt − 1, if Pt − Pt − 1> 0 and 0 otherwise) Trendj = ⎧ ⎨ ⎩TF , j = 2(Tdown = Pt − Pt − 1, if Pt − Pt − 1< 0 and 0 otherwise)
(3)
where TR and TF represents the rising and falling trend. In high-frequency volatility state, the returns of the rising and falling trend shown in Fig. 3 range from 0 to 2 and −1.6 to 0 respectively; in low-frequency volatility state, however, the returns shown in Fig. 4 range from 0 to 0.4 and −0.4 to 0 respectively, which manifests less volatility than that in high-frequency volatility state. 2.2. The identification model of the weekday effect Consider the heteroscedasticity of the carbon returns, this paper conducts the generalized autoregressive conditional heteroskedasticity (GARCH) model to measure the wandering weekday effect. We add the first order lag of returns into the regression equation to overcome the self-correlation of the carbon returns sequence.
Rt = Rt − 1 +
5
∑i =1 φi Dit + ɛ1t
i = 1, 2, 4, 5
(4)
where Rt,Rt-1 denotes the international carbon returns and the first order lag of returns. To avoid the virtual trap, this paper assumes Wednesday as a benchmark to measure only the returns volatility on Monday, Tuesday, Thursday, and Friday, i = 1, 2, 4, 5, and Dit represents daily dummy variable, if i = 1, means the trading day is Monday and D1t=1;D1t=0 otherwise. Other dummy variables are defined similarly. The fixed weekday effect does not include the moderation effect of market trends, AR (1)-GARCH (1,1) model is used to check the fixed weekday effect. The model is expressed as follows:
Rt = α 0 + α1 Rt − 1 +
5
∑i =1 φi Dit + ɛ3t
(5) 321
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Fig. 3. Volatility of the international carbon returns under the rising and falling trend in high-frequency volatility state.
Fig. 4. Volatility of the international carbon returns under the rising and falling trend in low-frequency volatility state. 2 2 σt2 = α 0 + α1 ɛ3, t − 1 + β1 σt − 1
(6)
To reflect the wandering weekday effect and capture the changing characteristics of carbon returns depicted in Fig. 3 and Fig. 4, we take the market trend as a moderator in the mean equation of the GARCH (1, 1) model. We identify the patterns of the wandering weekday effect by analyzing the cross-multiplication term of daily dummy variables and market trends. The model is T-AR (1)322
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Table 1 Descriptive statistics. Panel A: 2009.1.13–2017.7.28
Mean
Std. Dev
Skewness
Kurtosis
J-Bera
Prob
Monday Tuesday Wednesday Thursday Friday
−0.231 −0.018 0.112 −0.004 −0.112
2.876 3.217 2.806 2.862 3.197
1.844 −1.922 −0.24 −1.382 1.563
21.147 34.35 8.785 16.765 25.135
6058.36 18,289.57 617.873 3605.493 8953.538
0.000 0.000 0.000 0.000 0.000
Panel B: high-frequency volatility state
Mean
Std.Dev
Skewness
Kurtosis
J-Bera
Prob
Monday Tuesday Wednesday Thursday Friday
−0.441 −0.056 0.322 0.094 −0.169
4.542 5.28 4.586 4.773 5.365
1.418 −1.231 −0.291 −0.969 0.943
9.616 13.569 3.65 6.691 9.482
334.7 745.816 4.795 104.993 273.387
0.000 0.000 0.091 0.000 0.000
Panel C: low-frequency volatility state
Mean
Std.Dev
Skewness
Kurtosis
J-Bera
Prob
Monday Tuesday Wednesday Thursday Friday
−0.119 0.002 0.002 −0.052 −0.159
1.069 1.023 1.005 1.02 0.969
0.057 −0.061 −0.04 0.099 0.087
1.881 2.093 1.955 2.037 2.169
14.117 10.053 13.234 11.837 8.593
0.001 0.007 0.001 0.003 0.014
GARCH (1,1) and expressed as follows: 5
Rt = α 0 + α1 Rt − 1 +
2
5
2
∑ φi Dit + ∑ δj Trendjt + ∑ ∑ θij Trendj × Di + ɛ4t i=1
j=1 5
σt2 = α 0 + α1 ɛ24, t − 1 + β1 σt2− 1 +
i=1 j=1 2
5
2
∑ φi Dit + ∑ δj Trendjt + ∑ ∑ θij Trendj × Di i=1
j=1
(7)
i=1 j=1
(8)
where Dit and Trendj × Di represent daily returns and daily returns under the moderation effect of market trend respectively. For depicting the influence of market volatility, the variance is introduced into the mean equation of above models, and the referring model of AR (1)-GARCH (1,1)-M and T-AR (1)-GARCH (1,1)-M is obtained. To reflect the sensitivity of tail distribution to the wandering weekday effect, this article also conducts the empirical model under t and GED distribution respectively. Moreover, the AIC principle is used to determine the optimal distribution model. The smaller the AIC value, the better the model in reflecting the tail returns. 3. Empirical analysis 3.1. Descriptive statistics analysis The descriptive statistics of the sample are show in Table 1. For total sample and high-frequency volatility state, the highest average returns are on Wednesday, and the earnings on Monday are said to be the lowest. There is a significant peak fat-tailed phenomenon in all trading days, which indicates that the international carbon market does not conform to the laws of normal distribution. For low-frequency volatility state, the highest returns are observed on Tuesday and Wednesday, while the lowest are seen on Friday, the skewness is around 0 and the kurtosis is less than 3, those results show that the market is basically consistent with the normal distribution in low-frequency volatility state. 3.2. Analyzing the fixed weekday effect Empirical results recorded in Table 2 show that in high-frequency volatility state, there is a negative fixed Monday effect under the t and GED distribution. Additionally, the model AR (1)-GARCH (1,1)-M displays a better fitting performance according to the AIC minimum principle. However, when market in low-frequency volatility state, as shown in Table 3, the AR (1) -GARCH (1,1) model reflects a negative Friday effect under the t distribution, while under the GED distribution exhibits a negative Monday effect. Moreover, the fixed Monday effect under the GED distribution is shown to be more effective in depicting tail returns. Low-frequency volatility means lower risk of the returns, indicates no significant difference among daily returns, which reduces the impact of risk on daily earnings. Therefore, we can conclude that there is a significant negative fixed Monday effect in the international carbon market. However, the assumption behind the fixed weekday effect insist seasonal anomaly should become steady, that means the volatility of the returns of international carbon market is stable over time, which is contrary to the changing characteristics of returns depicted in Fig. 1 and Fig. 2, let alone reflect the return volatility under different market trends accurately. To overcome those defects, a 323
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Table 2 Testing the fixed weekday effect in high-frequency volatility state of the international carbon market. AR(1)-GARCH(1,1)
AR(1)-GARCH(1,1)-M
Coff-t
Coff-GED
Mean D1 D2 D4 D5 AIC R2
−0.935 −0.330 −0.205 −0.551 5.8479 0.0049
Vari ⁎⁎
0.132 3.449 2.383 0.941
Mean −0.818 −0.427 −0.194 −0.537 5.8633 0.0006
Coff-t Vari
⁎⁎
0.622 6.670* 5.667* 1.686
Coff-GED
Mean −0.956 −0.296 −0.182 −0.552 5.8441 0.004
⁎⁎
Vari
Mean
Vari
0.040 3.281 2.224 0.886
−0.817* −0.389 −0.158 −0.528 5.8658 0.0056
0.507 6.431 5.606* 1.640
Notes: The result is calculated according to the Eqs. (5) and (6). *, **, *** denote the statistical significance at 10%, 5%, and 1%. Table 3 Testing the fixed weekday effect in low-frequency volatility state of the international carbon market. AR(1)-GARCH(1,1)
AR(1)-GARCH(1,1)-M
Coff-t Mean D1 D2 D4 D5 AIC R2
−0.096 0.023 −0.034 −0.152* 2.8789 0.0094
Coff-GED Vari 0.133 0.030 0.031 −0.106
Mean −0.046 −0.024 −0.008 0.002 2.7135 0.0009
⁎⁎
Coff-t
Coff-GED
Vari
Mean
Vari
Mean
Vari
−0.037 0.013 0.010 −0.003
−0.031 0.031 −0.016 −0.197 2.8798 0.0099
0.134 0.017 0.025 −0.102
−0.065 −0.018 0.017 −0.088 2.7267 0.0059
−0.021 −0.018 −0.005 −0.006
Notes: The result is calculated according to the Eqs. (5) and (6). *, **, *** denote the statistical significance at 10% , 5% and 1%.
wandering weekday effect with the moderation of market trends under high and low frequency volatility state is tested. 3.3. Analyzing the wandering weekday effect 3.3.1. Analyzing the pattern of the wandering weekday effect By empirical analysis, we conclude that under the t distribution, when the market in high-frequency volatility state, as depicted in Table 4, there is a negative Monday and positive Tuesday effect. However, under the moderation of market trends, there is a positive wandering Monday and negative wandering Tuesday effect when the market rises, while manifests a negative wandering Monday and Table 4 Testing the wandering weekday effect in high-frequency volatility state of the international carbon market based on trend moderation effect. T-AR(1)-GARCH(1,1) Coff-t
D1 D2 D4 D5 TR TF TR*D1 TR*D2 TR*D4 TR*D5 TF*D1 TF*D2 TF*D4 TF*D5 AIC R2
T-AR(1)-GARCH(1,1)-M Coff-GED
Coff-t
Coff-GED
Mean
Vari
Mean
Vari
Mean
Vari
Mean
Vari
−1.362⁎⁎⁎ 0.828⁎⁎ 0.041 −0.653 10.579⁎⁎⁎ 11.906⁎⁎⁎ 3.601⁎⁎⁎ −2.838⁎⁎⁎ 0.531 4.044⁎⁎⁎ −4.168⁎⁎⁎ 3.682⁎⁎⁎ 0.342 0.388 4.0838 0.8215
−1.348 −3.699* −1.172 −3.337 −0.838 0.453 5.811 1.554 −4.221 −0.444 3.971 −6.845 −2.728 −0.395
−1.361 0.961 0.019 −0.711 10.618⁎⁎⁎ 11.888⁎⁎⁎ 3.474* −2.811* 0.567 4.599⁎⁎ −4.23⁎⁎ 4.169⁎⁎ 0.292 0.328 4.3726 0.8218
−1.195 −1.005 −0.781 −1.372 −0.882 0.300 −0.265 −0.890 −4.890 −1.500 4.435 0.078 −0.117 1.873
−0.933⁎⁎ 0.806⁎⁎ 0.170 0.160 11.863⁎⁎⁎ 13.051⁎⁎⁎ 4.442⁎⁎⁎ −1.040⁎⁎ 2.099* 1.848* −3.311⁎⁎⁎ 3.242⁎⁎⁎ 0.477 1.261 3.6951 0.7942
−2.464 −3.796* −3.630* −3.679* −0.073 0.562 0.195 1.685 1.850 0.580 2.672 −2.298 −1.004 −1.381
−1.032* 0.840 0.248 0.180 11.723⁎⁎⁎ 13.174⁎⁎⁎ 4.534⁎⁎⁎ −1.350 1.719 2.005 −3.528⁎⁎ 3.735⁎⁎ 1.246 1.997 3.7811 0.8007
−2.704 −3.588⁎⁎ −3.122* −3.693⁎⁎ −0.103 −0.393 0.012 0.844 −1.003 1.236 3.085 −2.051 −2.943 −0.771
Notes: The result is calculated by the Eqs. (7) and (8). *,⁎⁎,⁎⁎⁎denote the statistical significance at 10%, 5% and 1%. 324
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Table 5 Testing the wandering weekday effect in low-frequency volatility state of the international carbon market based on trend moderation effect. T-AR(1)-GARCH(1,1) Coff-t Mean D1 D2 D4 D5 TR TF TR*D1 TR*D2 TR*D4 TR*D5 TF*D1 TF*D2 TF*D4 TF*D5 AIC R2
0.011 0.048 −0.008 −0.013 7.781⁎⁎⁎ 6.996⁎⁎⁎ −0.921 −0.440 −0.620 −1.185 0.429 0.603 −0.426 −0.269 1.1091 0.7974
T-AR(1)-GARCH(1,1)-M Coff-GED
Vari −0.097* −0.086 −0.089* −0.070 −0.137 0.130 −0.156 −0.162 −0.304 −0.311 0.047 0.060 0.352 0.314
Mean 0.056 0.070 −0.017 −0.029 8.299⁎⁎⁎ 7.029⁎⁎⁎ −1.840⁎⁎⁎ −0.719 −0.432 −1.356⁎⁎ 0.628 1.418⁎⁎ −0.723 −0.411 1.1514 0.8012
Coff-t Vari
Mean
−0.067 −0.193⁎⁎⁎ −0.074 −0.061 0.145 0.126 −0.455⁎⁎⁎ 0.261 −0.517⁎⁎⁎ −0.560⁎⁎⁎ 0.188 −0.814* 0.396 0.335
0.005 −0.012 −0.022 −0.021 7.277⁎⁎⁎ 7.066⁎⁎⁎ −1.402⁎⁎ −0.683 −0.723 −1.260* 0.338 −0.006 −0.182 0.076 1.0484 0.7892
Coff-GED Vari ⁎⁎
−0.104 −0.144⁎⁎⁎ −0.082⁎⁎ −0.063 −0.117 0.144 −0.227 0.036 −0.299 −0.331 0.125 −0.076 0.320 0.339
Mean
Vari
−0.006 −0.039 −0.012 −0.009 7.183⁎⁎ 6.740⁎⁎ −1.254⁎⁎⁎ −0.714* −0.752⁎⁎ −1.115⁎⁎⁎ 0.299 −0.150 −0.198 −0.003 0.9977 0.7803
−0.097 −0.141⁎⁎ −0.082 −0.058 −0.141 0.151 −0.183 0.007 −0.276 −0.352 0.173 0.008 0.328 0.380
Notes: The result is calculated by the Eqs. (7) and (8). *,⁎⁎,⁎⁎⁎denote the statistical significance at 10%, 5% and 1%.
positive wandering Tuesday effect when the market falls. Under the GED distribution, the model T-AR(1)-GARCH(1,1) does not present any pattern of wandering weekday effect, while the T-AR(1)-GARCH(1,1)-M model displays a negative Monday effect and reverses to a positive wandering Monday effect when the market rises and remains a negative one when the market falls. Different models depict different patterns of wandering weekday effect under different distributions, while the T-AR(1)-GARCH(1,1)-M model is more effective under the t distribution based on the AIC principle. When the market in low-frequency volatility state, as in Table 5, the result suggests that there is no wandering weekday effect. Therefore, we conclude that the international carbon market has a positive wandering Monday and negative wandering Tuesday effect when the market rises and a negative wandering Monday and positive wandering Tuesday effect when market falls. 3.3.2. Comparing the performance of model between fixed and wandering weekday effect AIC is a standard to measure the performance of the statistical model. Furthermore, we find that the AIC value of wandering weekday effect in high and low frequency volatility state, which show in Table 4 and Table 5 are smaller than that of fixed weekday effect in Table 2 and Table 3. This conclusion also supports the claim that the wandering weekday effect is more accurate and reliable to describe daily volatility than fixed weekday effect, which is in line with the study conducted by Doyle and Chen (2009) and Boubaker et al. (2017). 3.4. Discussing the reasons of wandering weekday effect 3.4.1. Reasons from the settlement procedures and information disclosure system The settlement procedures and information disclosure system are popular reasons for the weekday effect of financial markets (Patel and Mallikarjun, 2014; Zhang et al., 2015). Frist, the settlement procedures followed in the international carbon market regulates that the carbon products delivery takes place 3 days after the last trading day according to the Intercontinental Exchange (ICE), which encourages frequent trading on Monday and Tuesday for reducing the opportunity cost and risk of futures holding, makes the gains of those two days significantly different from other trading days. Second, the information disclosure system according to the ICE rules that the trading suspension within weekend makes the gains of the following Monday and Tuesday contain more trading information and uncertainty than other days, increases price volatility, thereby making it easy to increase the motivation of speculation and trading on those days. This explanation has been convinced as a common reason of the weekday effect in other financial markets, including the carbon markets, which trading suspension within weekend (Zhang et al., 2015). Driven by those two reasons, investors' psychology and the resulting trading decisions usually show great difference under different volatility state and market trends. In high-frequency volatility state, when market is rising, the corresponding expected return is higher and investor confidence rises, the carbon market investors tend to increase their Monday's holdings, which results a substantial increase in earnings on Monday. However, high-frequency fluctuating characteristics of the market means the wandering Monday effect is usually not sustainable, investors will take risk hedging transactions and dispose carbon assets timely for risk aversion on Tuesday, resulting in a sharp decline of Tuesday's earnings, which form a negative wandering Tuesday effect. While when market is falling, the market prospect is not optimistic, the carbon market investors tend to take short sell deals and reduce the holding of carbon asset on Monday, which results a short decline of Monday's earnings. Driven by excess returns, however, investors are more likely to take reverse operations and prone to increase their Tuesday's holdings, which results a big boost of Tuesday's 325
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Table 6 Analyzing the determinants of the wandering Monday and Tuesday effect under the rising and falling trend of the carbon market.1 Rising-trend
wandering weekend effect Rt( − 20) Rt( − 120) Coal Power Oil Gas Macro R2
Falling-trend
Monday
Tuesday
Monday
Tuesday
4.442⁎⁎⁎ 0.0012 0.0172* 0.0031 0.0034 −0.0037 −0.0006 −0.0092 0.0939
−1.040⁎⁎ 0.0575⁎⁎ −0.0393 0.0344 −0.1998⁎⁎ −0.1114⁎⁎ −0.0964* 0.3997⁎⁎⁎ 0.0369
−3.311⁎⁎⁎ −0.0091⁎⁎⁎ −0.0105⁎⁎⁎ 0.0076 −0.0167 −0.0101 0.0016 0.0207 0.2465
3.242⁎⁎⁎ −0.0423⁎⁎⁎ −0.0132 0.0199 −0.1358 −0.0336 0.0422 0.2035 0.105
Notes: The result is calculated by the Eqs. (9) and (10). *,⁎⁎,⁎⁎⁎denote the statistical significance at 10%, 5% and 1%.
returns. In low-frequency volatility state, however, the return volatility is low, the market risk is controllable or affordable, and investors are prone to adopt long-term and stable investment strategies. Therefore, irrespective of whether the market is rising or falling, there is little change in daily returns and does not exhibit any patterns of wandering week effect. 3.4.2. Reasons from the determinants of carbon prices Plenty of researches have been convinced that the returns of international carbon market are closely related to the returns of energy market and macroeconomy (Byun and Cho, 2013; Zhang and Yang, 2016). As complementary investment products, carbon returns are negatively correlated with other energy returns. The macroeconomy usually show positively relationship with the energy consumption and carbon prices. Based on this, this paper selects the prices of coal, electricity, oil and natural gas, which are consumed in large amounts of the international energy market, and macroeconomic indicators to detect the determinants of the wandering Monday and Tuesday effect. The model is GARCH (1,1) and expressed as follows:
Di × Rt = γ1 Rt (−20) + γ2 Rt (−120) + γ3 Coal + γ4 Power + γ5 Oil + γ6 Gas + γ7 Marco + ɛ5t σt2
= α0 +
α1 ɛ5,2 t − 1
+
β1 σt2− 1
+ η1 Coal + η2 Power + η3 Oil + η4 Gas + η5 Marco
(9) (10)
Where Di × Rtrepresent the wandering weekday effect recognized by the Eqs. (7) and (8). Coal and Power are assumed to be Australia BJ coal spot prices and Basic European power index; Oil is replaced by Brent crude oil futures prices; Gas prices from the UK natural gas continuous futures prices; The European Stoxx 50 (Macro) is selected to indicate the macroeconomy. The returns adhere to the natural logarithm of price sequence. Furthermore,Rt( − 20)andRt( − 120) are replaced by the long and short terms of the returns from the past 1 and 6 months respectively. The results show (see Table 6) that when market is rising, the wandering Monday effect is influenced significantly by the longterm returns, while the wandering Tuesday effect is affected by the short-term returns. The historical returns of the carbon market are the most valuable reference for investors to make trading decisions on Monday. As a result, investors tend to continue the long-term trading strategies adopted on Mondays in the past, thereby the earnings of Monday positively related to the long-term earnings. While for Tuesday, investors can refer to Monday's trading decisions and other energy market information, so that the Tuesday's earnings are greatly influenced by short-term returns. Further research shows that the Tuesday's returns are also negatively related to electricity, oil and gas returns and positively related to the macroeconomy. When the market in high-frequency volatility state, the shortterm investors tend to adopt reverse arbitrage trading on Tuesdays after increasing the holdings on Monday. Therefore, as complementary investment products, the returns of electricity, oil, and gas on Tuesdays are negatively related to the carbon returns. For macroeconomic indicators, the better is the economic prospect, the faster the growth of the entity businesses and the carbon emissions will further promote the rise of the carbon prices. When the market is falling, however, the wandering Monday effect is only negatively affected by its long and short trend, while the wandering Tuesday effect is affected by its short trend and macroeconomy. Other energy prices and macroeconomic factors have little reference for investors' decision-making on Mondays when the carbon market depicts a falling trend. In fact, a brief decline in Monday's returns also provide a certain profit space for arbitrage and hedging transactions on Tuesdays. As a result, investors will increase their holding of carbon futures contracts on Tuesday driven by profit-seeking psychology in the short term. 4. Conclusions This paper focuses on the study of the wandering weekday effect of the international carbon market based on the perspective of market inefficiency, which overcome the defects of fixed weekday effect that seasonal anomaly should become steady over time. The results show that the international carbon market manifests a wandering weekday effect only in high-frequency volatility state, there 1 The data of Coal and Oil originate from the Wind database; Gas data from the ICE; Power data from the European electric power Exchange(EEX); Macro data from STOXX. The period is from January 12, 2009 to July 28, 2017.
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is a positive wandering Monday and negative wandering Tuesday effect when market is rising, and a negative wandering Monday and positive wandering Tuesday effect when market is falling. Further analysis shows that the settlement procedures, information disclosure system and the determinants of carbon returns, especially its long and short-trend and macroeconomy are stronger reasons for the wandering Mondays and Tuesdays effect. In research, we also confirm that the wandering weekday effect observed in the international carbon market is not robust to the choice of error distribution, which is supported by Boubaker et al. (2017) conclusions about the weekday effect with respect to the stock market. The study of the wandering weekday effect under the moderation of rising and falling trends in high and low frequency state is more reasonable and accurate to detect the volitionally of daily returns of the international carbon market. The patterns of wandering weekday effect encourage investors to take risk hedging and arbitrage trade driving by investors' attitudes and psychology to risk according to the prospect theory. As the improvement of the diversification of carbon investors, the profit space will be compressed, the carbon market will gradually return to the state of equilibrium, and then market efficiency will be promoted. To conclude, the findings of this article provide a new evidence against the Efficient Market Hypothesis and contribute to the decision-making and improvement of market efficiency in the international carbon market. Acknowledgment The authors thank the National Natural Science Foundation of China under Grant [71373065] for supporting this research work. Conflicts of interest None. References Baker, H.K., Rahman, A., Saudi, S., 2008. The day-of-the-week effect and conditional volatility: sensitivity of error distributional assumptions. Rev. Financ. 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