A Research on Cross-sectional Return Dispersion and Volatility of US Stock Market during COVID-19
11 A Research on Cross-sectional Return Dispersion and Volatility of US Stock Market during COVID-19
Jiawei Du
Abstract:
We studied the volatility and cross-sectional return dispersion effect of S&P Health Care Sector under the covid-19 epidemic. We innovatively used the Google index to proxy the impact of the epidemic and modeled the volatility. We also studied the influencing factors of the log-return of S&P Energy Sector and S&P Health Care Sector. We found that volatility is significantly affected by both the epidemic and cross-sectional return dispersion, and the coefficients in front of them are all positive, which means that the herding behaviour did not exist and as the cross-sectional return dispersion increases and the epidemic becomes more severe, the volatility of stock returns is also increasing. We also found that the epidemic has a significant negative impact on the return of the energy sector, and finally we provided our suggestions to investors.
Keywords:
COVID-19, Cross-sectional return dispersion, Volatility, Health care sector, Energy sector, GJR-Garch(1,1)-X, Garch(1,1)-X, EGarch(1,1)-X
Contents
1. Introduction ................................................................................................................................................... 4
2. Literature Review ........................................................................................................................................... 4
3. Data ................................................................................................................................................................ 6
4. Methodology .................................................................................................................................................. 8
5. Finding and Discussion ................................................................................................................................. 10
6. Conclusion and Suggestions ......................................................................................................................... 15
References: ...................................................................................................................................................... 16
Appendix A: Code ............................................................................................................................................. 18
Stata code .................................................................................................................................................... 18
Python CSAD and CSSD Calculation code .................................................................................................... 20
Python Plot ................................................................................................................................................... 22
Appendix B: Raw Data ...................................................................................................................................... 24
Short horizon................................................................................................................................................ 24
Long horizon................................................................................................................................................. 25
1. Introduction
Covid-19 epidemic swept the world in 2020, first in China, then in Japan, South Korea, Iran, Italy, Spain, the United Kingdom and the United States. The epidemic caused a sharp economic downturn. According to the information of the United States Department of Commerce, the real GDP of the United States fell by 4.8% in the first quarter. Herding and return dispersion have been studied by many researchers. Many literatures showed that herding exists widely in stock market, especially in developing countries (Chiang, T. C., and Zheng, D.,2010). In this paper, we want to explore whether there is herding effect in American stock market, whether the epidemic has an impact on the return of American stock market, and what factors affect the stock volatility in this period. Different from the similar research, we not only use the traditional indicators such as the number of infected persons to represent the abstract variable of epidemic situation, but also use Google index to represent it, which enables us to better reflect the real impact of the epidemic situation when the data of COVID-19 in the United States is distorted in the early stage of the epidemic. In terms of sector selection, we selected S&P 500 health care sector and energy sector for comparison, and calculated their respective CSAD and CSSD indexes. Since the outbreak time in the United States is very close to now, and the epidemic is still developing, we chose two time periods, namely short time horizon from March 2 to May 29 (63 time observations), and long time horizon from February 20, 2020 to June 12, 2020 (80 time observations). The basis for this choice will be explained later. Finally, we will make investment suggestions to investors on our results.
2. Literature Review
Chang, E. C., Cheng, J. W., and Khorana, A. (2000) have made a remarkable contribution to the study of herd behaviour and herd behaviour. They have found that herd behaviour is more obvious in some emerging markets than in mature markets, especially during periods of rising market prices. Not only normal investors, Choi, N., and Sias, R. W. (2009) found that herding behaviour also existed in institutional investors. Fei, T., Liu, X., and Wen, C. (2019) regarded the cross-sectional stock return dispersion as a kind of herd behaviour indicator like previous researchers did, the cross-sectional return dispersion index in our later paper refers to their research . Maio, P. (2016) studied the relation between stock return dispersion and the future stock return, he found that compared with other indicators, return dispersion have a stronger prediction, especially for the large-scale stocks and growth stocks. Prior to this, Stivers, C. T. (2003) conducted similar studies, but he used data on monthly returns dispersion. He also studied the relationship between returns dispersion and future volatility, and found that these relationships are very significant. Chortareas, G., Jiang, Y., and Nankervis, J. C. (2011) focus on the euro volatility, and they found that data with high-frequency and long-time horizon could improve volatility forecasting performance significantly. In terms of the method for studying volatility, the conventional models are the ARCH model (Engle, R. F. ,1982) and GARCH model (Bollerslev, T. ,1986), but many researchers have used the improved model of the GARCH model. For example, Hwang*, S., and Satchell, S. E. (2005) have used the GARCHX model. Many researchers also used the GJR-Garch model proposed by Glosten et al. (1993) or the TGARCH model proposed by Zakoian (1994) or the EGARCH proposed by Nelson and Cao (1991). Fei, T., Liu, X., and Wen, C. (2019) chose the GARCH, GJR-GARCH, and HAR model, one of their findings is that the cross-sectional stock return dispersion did have significant influence on the forecast volatility. Onali, E. (2020) did a very updated research on the relation between the stock volatility and COVID-19 epidemic, he added the COVID-19 factor both into mean equation and volatility equation of the Garch(1,1) model, interestingly, he first regarded the increasing infections in Iran as a good index for American stock market, while in the end, he did not find the significance. Even, the infections and deaths cases from most of the countries (include America itself) he studied showed no influence on the US stocks returns, but showed significant influence on volatility.
In December 2019, an unexplained pneumonia virus outbreak occurred in Wuhan. The epidemic was first discovered in the Wuhan South China Seafood Wholesale Market. With the development of the epidemic, infected people also appeared in other provinces in China and in other countries (Li et al. 2020). On February 11, 2020, WHO named the virus COVID-19. One month later, on March 12, 2020, the National Health Commission of China announced that the peak period of the covid-19 epidemic had passed, but other countries represented by US, Iran, Italy, and South Korea had an outbreak. At about the same time, WHO announced covid-19 Epidemic Global Pandemic. Data from Johns Hopkins University, as of April 28, more than 1 million people in the United States were infected with COVID-19, and more than 2 million as of June 8.
The data left behind by web searches for research and prediction has a long history. H. A. Johnson et al. (2004) collected the visit data of health-related websites and found that the number of visitors of flu-related articles and other flu-related data had a strong correlation with the influenza number data provided by the CDC. Later, j. Ginsberg et al. (2009) studied the relationship between Google search data and the incidence of influenza diseases, and found that through the modeling of the two, the outbreak of influenza could be predicted 1-2 weeks in advance of the traditional method. N. Askitas et al. (2009) took the unemployment rate of Germany as the research object. He conducted statistical analysis on the keywords related to unemployment rate in Google search and found that these keywords had a strong correlation with the actual unemployment rate. N. P. Lincoln (2011) studied the sales volume of apple's electronic products and empirically obtained the significant correlation between the sales volume of apple's electronic products and the Internet search data of Google by using the Internet search data provided by Google search. We have reasons to believe that we can use Google index data to estimate the extent of the covid-19 epidemic.
3. Data
Stocks data we chose the constituent stocks in the S&P 500 Health Care Sector and S&P 500 Energy Sector from Yahoo Finance, time horizon from Feb 20, 2020 to June 12 th , 2020 (80 time-observations). Also, we chose the time horizon from Mar 2 nd to May 29 th (63 time-observations), during which, Covid-19 in America is very severe, and after that, there was a large black march in the United States, which had a certain impact on our variables such as VIX and stock returns. It would be more scientific to select a narrower period. In this paper, we focus on the three important factors. First is COVID-19. The herding behavior we study is in the context of the COVID-19 epidemic, thus, we need to choose a proxy to represent the COVID-19. One is easy to understand, the infections in the US, we take the log of it (ln(1+x)) , namely, ‘Inlg’. However, the lack of nucleic acid testing reagent and people's lack of awareness in the early stage of the epidemic in the United States caused distortion of the data, we should find another proxy to represent it, finally, we choose Google Index with keywords ‘COVID - hy we choose it? The impact of the COVID-19 epidemic is twofold. On the one hand, it is the practical impact, such as the direct economic impact caused by the inability of infected people to work and the inability of factories or companies to function normally. On the other hand, the impact of the epidemic on people's psychology. Once people panic about the COVID-19 epidemic, they will reduce their consumption and sell assets such as stocks, causing indirect economic losses. The increase in the number of covid-19 infections and people's fear of the epidemic are both contributing to the rise of the Google index. Therefore, we believe that the Google index can better reflect the true impact of the epidemic with the distortion of the epidemic data. We take the log of it (ln(1+x)) as ‘Golg’. A lso, we take log of (ln(1+x)) VIX Index, as another kind of panic indicator. In simple terms, see the table below. Table 1 Proxy Definition Comment Whether it can reflect the epidemic situation
Inlg
The log of Infections Data distortion Yes
Golg
The log of Google Index Reflect both the number of infections and investors’ panic about the epidemic Yes
VIXlg
The log of VIX Index Reflect investors' panic Partial
The second important factor is herding behavior, one of our targets. We followed Christie and Huang (1995) and use CSAD and CSSD to represent it.
CSSD 𝑡 = √∑(𝑟 𝑖,𝑡 − 𝑟 𝑚,𝑡 ) /(𝐾 − 1) 𝐾𝑖=1 (1)
CSAD 𝑡 = ∑ |𝑟 𝑖,𝑡 − 𝑟 𝑚,𝑡 | 𝐾𝑖=1
𝐾 (2)
Where 𝑟 𝑚 is the mean log-return. The log-return, CSAD and CSSD plot see Figure 1 and 2. The third important factor is the estimation of volatility. We use the Garch(1,1)-X model, EGarch(1,1)-X model and the GJR-arch(1)-X model. In next part, we will introduce it. For convenience, Table 2 showed the introduction of parameters. Table 2 Parameter Introduction Splg
The first order differential of S&P 500 Index log-return
Hclg
The first order differential of S&P 500 HealthCare Sector Index log-return
Elg
The first order differential of S&P 500 Index Energy log-return
Inlg
The first order differential of log-infections
Golg
The first order differential of log-Google-Index
Vixlg
The first order differential of log-VIX-Index
Hccsad
CSAD of S&P 500 HealthCare Sector
Hccssd
CSSD of S&P 500 HealthCare Sector
Ecsad
CSAD of S&P 500 Energy Sector
Ecssd
CSSD of S&P 500 Energy Sector
4. Methodology
Before the establish of the model, we need to do the ADF Test and normal distribution test first, the Table 3 and 3 showed the test results. In Table 3, we see that except ‘Hccsad’ and ‘Hccssd’ , all the variables showed the P-value less than 0.01, since the dataset is small, we still believed that the ‘Hccsad’ and ‘Hccssd’ (P-value less than 0.1) do not exist unit root, they are stationary. Data with longer time horizon are more significant. Table 4 showed the ‘sktest’ results, we regarded the distribution of the ‘hclg’ residual sequence as normal distribution while ‘elg’ as ‘t - distribution’ (later arch-LM test rejected the arch effect, we ended up abandoning it). Table 3. ADF Test Parameter t-statistic 63 time-observations t-statistic 80 time-observations 1% Critical 5% Critical 10% Critical P-Value 63 time-obs. P-Value 80 time-obs. Splg (S&P 500 Index) -12.175 -13.212 -3.58 -2.93 -2.6 0.0000 0.0000
Hclg -12.324 -12.956 0.0000 0.0000
Elg -10.012 -10.091 0.0000 0.0000
Inlg -9.156 -8.677 0.0000 0.0000
Golg -4.564 -7.376 0.0002 0.0002
Vixlg -10.439 -10.495 0.0000 0.0000
Hccsad -2.612 -3.191 0.0905 0.0205
Hccssd -2.612 -3.191 0.0905 0.0205
Ecsad -7.92 -4.978 0.0000 0.0000
Ecssd -7.92 -4.962 0.0000 0.0000
Table 4. Normal Distribution Test
63 time-observations
80 time-observations
Parameter P-Value (Skewness) P-Value (Kurtosis) Joint P-Value P-Value (Skewness) P-Value (Kurtosis) Joint P-Value Splg
Hclg
Elg
Inlg
Golg
Vixlg
Hccsad
Hccssd
Ecsad
Ecssd
Another test is also needed, arch-LM test. We conduct it to verify if exist ‘arch’ effect. The p-value of the ‘hclg’ with short time horizon is , long horizon is 0.0004. There exists ‘arch’ effect. For ‘elg’, the p -value are 0.8580 and 0.7475 respect ively, ‘elg’ did not exist ‘arch’ effect.
Garch (1,1)-X Model: 0 𝑦 𝑡 = 𝛽 + 𝜖 𝑡 (3) 𝜎 𝑡2 = 𝛼 + 𝛼 𝜖 𝑡−12 + 𝛽 𝜎 𝑡−12 + 𝛾 𝑥 𝑡 (4) Where we use Inlg, Golg, VIXlg, HCcsad, HCcssd, LaggedHCcsad and LaggedHCcssd as 𝑥 𝑡 respectively. Besides, for comparation, we would fit the data by two time-horizons. Time one from Mar 2nd to May 29 th and time two from Feb 20 th to June 12 th . EGarch (1,1)-X Model: Mean equation is the same with the GARCH(1,1)-X model. And volatility term has been written as: ln(𝜎 𝑡2 ) = 𝜔 + 𝛼 (𝜙𝜂 𝑡−1 + 𝛾(|𝜂 𝑡−1 | − 𝐸|𝜂 𝑡−1 |)) + 𝛽 ln(𝜎 𝑡−12 ) + 𝜆 𝑥 𝑡 (5) Where 𝜂 𝑡 is i.i.d. standardized random variables with N(0,1). Still, we would fit the data by two time-horizons. GJR-Garch (1,1)-X Model: 𝜎 𝑡2 = 𝛼 + 𝛼 𝑢 𝑡−12 + 𝛽 𝜎 𝑡−12 + 𝛾𝑢 𝑡−12 𝐼 𝑡−1 + 𝜆 𝑥 𝑡 (6) Where 𝐼 𝑡−1 = 1 if 𝑢 𝑡−1 < 0 and = 0 if 𝑢 𝑡−1 ≥ 0 In addition, we also want to study if the COVID-19 and lagged return dispersion affect the log return of Health Care Sector and Energy Sector, since we suspect that the epidemic will have a negative impact on energy stocks and a positive impact on health care stocks. Therefore, we establish the multiple linear regression model. 𝑦 𝑡 = 𝛽 + 𝛽 𝑥 + 𝛽 𝑥 + 𝛽 𝑥 + 𝜖 𝑡 (7) Where 𝑥 is the S&P 500 Index, 𝑥 is the COVID-19 proxy, 𝑥 is the return dispersion index (we use CSAD here due to the results are very closed).
5. Finding and Discussion
Table 5 and 6 showed the Garch-X(1,1) results, and table 7 and 8 showed EGarch-X(1,1) results. Both the models fit narrower time horizon data well, we think that is because the narrow time horizon is the most severe time period in the United States during COVID-19, after which, the stock market has digested many factors of the epidemic and there were protests against racism in the United States, and these protests may affect our proxies and stock returns. The time before march, COVID-19 infections are very low in the United 1 States, which also affect the model performance, that is why we could not run the results when using long time horizon.
Table 5. Garch-X(1,1) Health Care Sector 63 time-observations from Mar 2 nd to May 29 th Parameter Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Garch-X(1,1) with Het Inlg Golg VIXlg HCcsad HCcssd Lagged HCcsad Lagged HCcssd arch_L1 garch_L1 cons
Inlg
Golg / 10.26219 (0.000) / / / / /
VIXlg / / 0.0963391 (0.000) / / / /
HCcsad / / / 174.414 (0.000) / / /
HCcssd / / / / 21.63075 (0.000) / /
LaggedHCcsad / / / / / 158.7028 (0.000) /
LaggedHCcssd / / / / / / 19.68188 (0.000)
Het_cons -322.54790 -10.10167 0.00366 -12.42266 -12.42266 -12.49498 -12.49653
Table 6. Garch-X(1,1) Health Care Sector 80 time-observations from Mar 2 nd to May 29 th Parameter Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Garch-X(1,1) with Het Inlg Golg VIXlg HCcsad HCcssd Lagged HCcsad Lagged HCcssd arch_L1 / -0.0417931 (0.530) -0.0417931 (0.530) 0.2325071 (0.002) 0.2325070 (0.002) garch_L1 cons -0.0010149 -0.0010149 0.0004675 0.0004675
Inlg / / / /
Golg / / / /
VIXlg / / / /
HCcsad
HCcssd / 16.79133 (0.000) / /
LaggedHCcsad / / 70.49632 (0.154) /
LaggedHCcssd / / / 7.784415 (0.154)
Het_cons -9.395639 -9.395639 -10.69531 -10.69531
Remark: Garch-X(1,1) with Het Inlg, Golg, VIXlg: Stata cannot run the results. 2 In table 5, the coefficients of the arch term and ‘ Garch ’ term are very significant in all the models from model significantly positive, which implies that the COVID-19 affects the stock market volatility significantly, when COVID-19 more severe, investors more panic, and the stock volatility get higher. For herding behavior index, CSAD and CSSD, whether it is the current CSAD(CSSD) or the CSAD(CSSD) lagging one period, the coefficients in front of them are significantly positive, which means that there is no herding effect. But as far as these two indicators are concerned, the return dispersion has led to an increase in volatility. We believe that the reason could be that US dollar assets are safe-haven assets, and this COVID-19 epidemic is a global epidemic. When the global asset risk increases, Investors will increase the allocation of U.S. dollar assets, resulting in the negative factors caused by the epidemic and the positive factors brought about by risk aversion repeatedly affecting the market, resulting in return dispersion and rising volatility. In table 7, the coefficients of ‘ egarch_a_L1 ’ and ‘ egarch_L1 ’ are significant in model 1, 6 and 7, which indicate there exist the leverage effect, however, as for the whole, we cannot say that the leverage effect is significant. Table 8 showed part of the results. Some models Stata does not run the results, also, the ‘ earch ’ term of the model with current CSAD(CSSD) and vixlg are not significant. Meanwhile, these three models are not the focus of our discussion, so we will not discuss them here. Table 7. EGarch-X(1,1) Health Care Sector 63 obs.
Parameter Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 EGarch-X(1,1) with Het Inlg Golg VIXlg HCcsad HCcssd Lagged HCcsad Lagged HCcssd earch_L1 -0.1007196 (0.485) -0.443223 (0.709) -0.327248 (0.294) -0.132522 (0.722) -0.132522 (0.722) -0.0962005 (0.575) -0.096201 (0.575) egarch_a_L1 egarch_L1 cons
Inlg
Golg / 4.585414 (0.381) / / / / /
VIXlg / / 0.0679617 (0.003 ) / / / /
HCcsad / / / 52.97203 (0.185) / / /
HCcssd / / / / 6.569569 (0.185) / /
LaggedHCcsad / / / / / 21.23671 (0.462) /
LaggedHCcssd / / / / / / 2.633768 (0.462)
Het_cons Table 8. EGarch-X(1,1) Health Care Sector 80 obs.
Parameter Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 EGarch-X(1,1) with Het Inlg Golg VIXlg HCcsad HCcssd Lagged HCcsad Lagged HCcssd earch_L1 / -0. egarch_a_L1 egarch_L1 -0. cons
Inlg / / /
Golg / / /
VIXlg
HCcsad / 92.1735 (0.066) /
HCcssd / / 14.53105 (0.002)
LaggedHCcsad / / /
LaggedHCcssd / / /
Het_cons -11.94937 -5.589827 -5.589826
Remark: EGarch-X(1,1) with Het Inlg, Golg, LaggedHCcsad, LaggedHCcssd: Stata cannot run the results. Table 9 showed the GJR-Garch-X(1,1) results, compared with Egarch(1,1)-X, GJR model showed that the leverage effect (‘ tgarch_a_L1’ term) is not significant, partly confirmed the results of the Egarch(1,1)-X model. We think the reason is that the COVID-19 epidemic is both good and bad effect for the stocks in health care. On the one hand, the epidemic makes the production of enterprises slow down and the economy under pressure. On the other hand, the market demand for the medical industry increases at this time, and finally the leverage effect is not significant. Nevertheless, of all the seven GJR-Garch-X(1,1) models, we are pleased that the X t term of volatility estimation are very significant, findings like Garch-X(1,1) model, Covid-19 has a positive impact on the volatility of the U.S. stock market. Herding effect is not significant during this period, but the dispersion of returns makes the volatility of stock returns increase. 4 Table 9. GJR-Garch-X(1,1) Health Care Sector 63 obs.
Parameter Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 EGarch-X(1,1) with Het Inlg Golg VIXlg HCcsad HCcssd Lagged HCcsad Lagged HCcssd arch_L1 tgarch_a_L1 -0.0042664 (0.992) -0.636893 (0.056) 0.163735 (0.597) -0.170801 (0.655) -0.170801 (0.655) 0.1276745 (0.809) 0.1276746 (0.809) garch_L1 cons
Inlg
Golg / 6.015732 (0.000) / / / / /
VIXlg / / 17.25633 (0.000 ) / / / /
HCcsad / / / 174.8302 (0.000) / / /
HCcssd / / / / 21.68237 (0.000) / /
LaggedHCcsad / / / / / 156.6696 (0.000) /
LaggedHCcssd / / / / / / 19.43011 (0.000)
Het_cons -591.0957 -7.521036 -11.03359 -12.46458 -12.46458 -12.4791 -12.4791
Table 10. Multiple linear regression model Market factor COVID-19 factor Return dispersion factor SPlg Golg Inlg LaggedHCcsad Hclg (63 obs.)
Model 1
Model 2
Hclg (80 obs.)
Model 1
Model 2
Elg (63 obs.)
Model 1
Model 2
Elg (80 obs.)
Model 1
Model 2
Table 10 showed the results of multiple linear regression. From it, we found that except the market factor ‘splg’ , both COVID-19 factor and return dispersion factor did not show the significant result on stocks in 5 Health Care sector. But for Energy Sector, COVID-
19 factor ‘inlg’ in mode l 2 of 63 time-observations regression and ‘golg’ in model 1 of 80 time-observations showed the negative significant relation with the ‘elg’.
Which partly confirm our conjectures. However, cross-sectional return dispersion(lagged) showed no relation with stock return.
6. Conclusion and Suggestions
We have the three main conclusion. The first conclusion is that herding does not exist (in terms of S&P health care sector), however, the coefficients in front of CSAD(lagged) and CSSD(lagged) are significantly positive, which showed that cross-sectional return dispersion increased the volatility of stock returns. The second conclusion is that the COVID-19 epidemic had a significant positive impact on the stocks return volatility of health care sector. The higher the number of infections and Google search volume, the higher the stocks return volatility. The third conclusion is that the return-dispersion with lags one period has no significant impact on stock returns during the epidemic. The impact of the epidemic on different sectors is different, it has no significant impact on the health care sector, but has a significant negative impact on the energy sector.
We have three suggestions for investors. The first one is that investors can short the energy sector during the pandemic, and the specific operation basis can be the freely available Google index (with keywords COVID-19). The second suggestion is that for risk-averse investors, investment in the stock market should be reduced during the COVID-19 outbreak, because the volatility will increase with the development of the epidemic. The third suggestion is, for risk averse investors, if the return dispersion of the previous day is high, they can sell stocks or hedge stocks today to reduce the negative effects of high volatility. And for high-frequency traders, they can enter the market today to seek trading opportunities with high volatility. References:
Askitas, N., & Zimmermann, K. F. (2009). Google econometrics and unemployment forecasting. Chang, E. C., Cheng, J. W., & Khorana, A. (2000). An examination of herd behavior in equity markets: An international perspective.
Journal of Banking & Finance , 24(10), 1651-1679. Carneiro, H. A., & Mylonakis, E. (2009). Google trends: a web-based tool for real-time surveillance of disease outbreaks.
Clinical infectious diseases , 49(10), 1557-1564. Chiang, T. C., & Zheng, D. (2010). An empirical analysis of herd behavior in global stock markets.
Journal of Banking & Finance , 34(8), 1911-1921. Choi, N., & Sias, R. W. (2009). Institutional industry herding.
Journal of Financial Economics , 94(3), 469-491. Chortareas, G., Jiang, Y., & Nankervis, J. C. (2011). Forecasting exchange rate volatility using high-frequency data: Is the euro different?.
International Journal of Forecasting , 27(4), 1089-1107. Christie, W. G., & Huang, R. D. (1995). Following the pied piper: Do individual returns herd around the market?.
Financial Analysts Journal , 51(4), 31-37.
COVID-19 United States Cases by County , (2020). [Online]. Available from: https://coronavirus.jhu.edu/map.html (Accessed: 14 June 2020). Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.
Econometrica: Journal of the Econometric Society , 987-1007. Hwang*, S., & Satchell, S. E. (2005). GARCH model with cross-sectional volatility: GARCHX models.
Applied Financial Economics , (3), 203-216. Fei, T., Liu, X., & Wen, C. (2019). Cross-sectional return dispersion and volatility prediction. Pacific-Basin Finance Journal , 58, 101218. Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks.
The journal of finance , 48(5), 1779-1801. Johnson, H. A., Wagner, M. M., Hogan, W. R., Chapman, W. W., Olszewski, R. T., Dowling, J. N., & Barnas, G. (2004). Analysis of web access logs for surveillance of Influenza. In
Medinfo (pp. 1202-1206). Lincoln, N. P. (2011).
The relationship between internet marketing, search volume, and product sales (Doctoral dissertation, The Ohio State University). Maio, P. (2016). Cross-sectional return dispersion and the equity premium.
Journal of Financial Markets , , 87-109. Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica . 59 (2): 347 –
370 Onali, E. (2020). Covid-19 and stock market volatility.
Available at
SSRN 3571453. 7 Stivers, C. T. (2003). Firm-level return dispersion and the future volatility of aggregate stock market returns.
Journal of Financial Markets , (3), 389-411. Zakoian, J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and control , 18(5), 931-955. 8
Appendix A: Code
Stata code gen date2=date(date,"YMD") gen helg=hclg-elg tsset date2 *ADF Test dfuller splg dfuller hclg dfuller elg dfuller inlg dfuller golg dfuller vixlg dfuller hccsad dfuller hccssd dfuller ecsad dfuller ecssd dfuller laggedhccsad dfuller laggedhccssd dfuller laggedecsad dfuller laggedecssd Normal-Distribution Test sktest splg sktest hclg sktest elg sktest inlg sktest golg sktest vixlg sktest hccsad sktest hccssd sktest ecsad 9 sktest ecsad sktest laggedhccsad sktest laggedhccssd sktest laggedecsad sktest laggedecssd *Garch(1,1)X arch hclg, arch(1) garch(1) vce(robust) het(inlg) arch hclg, arch(1) garch(1) vce(robust) het(golg) arch hclg, arch(1) garch(1) vce(robust) het(vixlg) arch hclg, arch(1) garch(1) vce(robust) het(hccsad) arch hclg, arch(1) garch(1) vce(robust) het(hccssd) arch hclg, arch(1) garch(1) vce(robust) het(laggedhccsad) arch hclg, arch(1) garch(1) vce(robust) het(laggedhccssd) *EGarch(1,1)X arch hclg, earch(1) egarch(1) vce(robust) arch hclg, earch(1) egarch(1) vce(robust) het(inlg) arch hclg, earch(1) egarch(1) vce(robust) het(golg) arch hclg, earch(1) egarch(1) vce(robust) het(vixlg) arch hclg, earch(1) egarch(1) vce(robust) het(hccsad) arch hclg, earch(1) egarch(1) vce(robust) het(hccssd) arch hclg, earch(1) egarch(1) vce(robust) het(laggedhccsad) arch hclg, earch(1) egarch(1) vce(robust) het(laggedhccssd) *GJR- Garch(1,1)X arch hclg, arch(1) tarch(1) garch(1) vce(robust) het(inlg) arch hclg, arch(1) tarch(1) garch(1) vce(robust) het(golg) arch hclg, arch(1) tarch(1) garch(1) vce(robust) het(vixlg) arch hclg, arch(1) tarch(1) garch(1) vce(robust) het(hccsad) arch hclg, arch(1) tarch(1) garch(1) vce(robust) het(hccssd) arch hclg, arch(1) tarch(1) garch(1) vce(robust) het(laggedhccsad) arch hclg, arch(1) tarch(1) garch(1) vce(robust) het(laggedhccssd) 0 * Multiple linear regression reg hclg splg golg laggedhccsad reg hclg splg inlg laggedhccsad reg elg splg golg laggedecsad reg elg splg inlg laggedecsad
Python CSAD and CSSD Calculation code
Python Plot
Appendix B: Raw Data
Short horizon date hclg golg inlg splg vixlg hc sp go newinfectionnewdeath newcure vix date2 hccsad ecsad hccssd ecssd elg laggedecssdlaggedecsadlaggedhccssdlaggedhccsadhelg vollg2020/3/2 0.04713 0.336472 1.38629 0.045011 -0.18247 1127.57 3090.23 7 20 0 1 33.42 21976 0.013303 0.006162 0.107265 0.049687 0.029118 0.075881 0.009411 0.11848 0.014694 0.018012 -0.294952020/3/3 -0.025773 0 -0.16252 -0.02851 0.096887 1098.88 3003.37 7 17 0 4 36.82 21977 0.012863 0.006125 0.10372 0.049387 -0.03171 0.049687 0.006162 0.107265 0.013303 0.005939 -0.003212020/3/4 0.056496 0 0.162519 0.041336 -0.14062 1162.75 3130.12 7 20 0 3 31.99 21978 0.016359 0.006403 0.131908 0.051628 0.021967 0.049387 0.006125 0.10372 0.012863 0.03453 -0.232882020/3/5 -0.024243 0.251314 0.559616 -0.03451 0.213911 1134.9 3023.94 9 35 0 2 39.62 21979 0.013585 0.005064 0.109538 0.040834 -0.03682 0.051628 0.006403 0.131908 0.016359 0.012572 0.1018822020/3/6 -0.005195 0.200671 0.721318 -0.0172 0.056906 1129.02 2972.37 11 72 0 3 41.94 21980 0.012842 0.019821 0.103551 0.159823 -0.05777 0.040834 0.005064 0.109538 0.013585 0.052576 0.1614012020/3/9 -0.05328 0.310155 0.171358 -0.07901 0.261226 1070.44 2746.56 15 127 0 3 54.46 21983 0.016663 0.067133 0.134354 0.541309 -0.22417 0.159823 0.019821 0.103551 0.012842 0.170892 0.251182020/3/10 0.034099 0.287682 0.132547 0.048215 -0.14096 1107.57 2882.23 20 145 0 4 47.3 21984 0.015939 0.01979 0.128522 0.159569 0.048743 0.541309 0.067133 0.134354 0.016663 -0.01464 -0.09812020/3/11 -0.039879 0.371564 0.682748 -0.0501 0.13062 1064.27 2741.38 29 287 0 5 53.9 21985 0.01986 0.0194 0.160136 0.156426 -0.05615 0.159569 0.01979 0.128522 0.015939 0.016274 -0.034892020/3/12 -0.076997 0.56453 0.105709 -0.09995 0.336605 985.4 2480.64 51 319 0 7 75.47 21986 0.025621 0.022704 0.206588 0.183069 -0.1312 0.156426 0.0194 0.160136 0.01986 0.054203 0.180112020/3/13 0.067224 0.057158 0.467257 0.088808 -0.26623 1053.92 2711.02 54 509 21 3 57.83 21987 0.027348 0.016429 0.220515 0.132472 0.08472 0.183069 0.022704 0.206588 0.025621 -0.0175 -0.066822020/3/16 -0.105274 0.258574 0.11145 -0.12765 0.357591 948.61 2386.13 79 787 0 9 82.69 21990 0.041637 0.019592 0.33573 0.157977 -0.14649 0.132472 0.016429 0.220515 0.027348 0.041218 -0.059512020/3/17 0.060676 -0.01274 0.494944 0.058226 -0.08555 1007.95 2529.19 78 1291 0 21 75.91 21991 0.037683 0.026954 0.303846 0.217335 0.007219 0.157977 0.019592 0.33573 0.041637 0.053457 0.0715252020/3/18 -0.03456 0.085942 0.125072 -0.05322 0.007088 973.71 2398.1 85 1463 50 26 76.45 21992 0.038604 0.036686 0.311275 0.295809 -0.1541 0.217335 0.026954 0.303846 0.037683 0.119543 0.0464352020/3/19 -0.018837 0.068208 1.00305 0.004697 -0.05997 955.54 2409.39 91 3989 2 37 72 21993 0.04341 0.028476 0.350023 0.229609 0.065288 0.295809 0.036686 0.311275 0.038604 -0.08413 -0.096962020/3/20 -0.041616 0.02174 -0.03236 -0.04433 -0.08641 916.59 2304.92 93 3862 13 51 66.04 21994 0.032188 0.017809 0.25954 0.143601 0.009585 0.229609 0.028476 0.350023 0.04341 -0.0512 0.129422020/3/23 -0.05103 0.040822 0.477721 -0.02973 -0.06976 870.99 2237.4 100 12072 0 127 61.59 21997 0.029307 0.021221 0.236313 0.171109 -0.06884 0.143601 0.017809 0.25954 0.032188 0.017805 -0.20042020/3/24 0.073138 -0.08338 -0.50755 0.089683 0.001298 937.08 2447.33 92 7267 0 113 61.67 21998 0.031817 0.019031 0.256549 0.153454 0.151108 0.171109 0.021221 0.236313 0.029307 -0.07797 0.0194222020/3/25 0.012577 -0.02198 0.189247 0.011469 0.036304 948.94 2475.56 90 8781 176 211 63.95 21999 0.034306 0.016897 0.276616 0.136241 0.043948 0.153454 0.019031 0.256549 0.031817 -0.03137 0.0933312020/3/26 0.067476 0.03279 0.464036 0.060544 -0.04723 1015.18 2630.07 93 13966 265 249 61 22000 0.020117 0.011421 0.162211 0.092087 0.060576 0.136241 0.016897 0.276616 0.034306 0.006899 -0.066432020/3/27 -0.02442 0 0.185646 -0.03427 0.071787 990.69 2541.47 93 16815 134 255 65.54 22001 0.017299 0.016838 0.139485 0.135771 -0.07182 0.092087 0.011421 0.162211 0.020117 0.047401 -0.224472020/3/30 0.045666 0.052922 -0.0593 0.032967 -0.13821 1036.98 2626.65 97 18856 2253 376 57.08 22004 0.018129 0.016359 0.146177 0.131906 0.010289 0.135771 0.016838 0.139485 0.017299 0.035377 -0.075092020/3/31 -0.003942 -0.02083 0.156028 -0.01614 -0.06403 1032.9 2584.59 95 22040 1080 604 53.54 22005 0.01531 0.015419 0.123451 0.12433 0.0162 0.131906 0.016359 0.146177 0.018129 -0.02014 0.1337112020/4/1 -0.039375 0 0.084736 -0.04515 0.063674 993.02 2470.5 95 23989 1196 911 57.06 22006 0.024046 0.01072 0.193885 0.086435 -0.04748 0.12433 0.015419 0.123451 0.01531 0.008109 -0.099222020/4/2 0.027474 -0.03209 0.117093 0.022573 -0.11404 1020.68 2526.9 92 26969 1531 1056 50.91 22007 0.023697 0.014973 0.191075 0.120733 0.086851 0.086435 0.01072 0.193885 0.024046 -0.05938 0.0818152020/4/3 -0.009658 -0.04445 0.36203 -0.01525 -0.08418 1010.87 2488.65 88 38734 687 1395 46.8 22008 0.015344 0.014307 0.123725 0.115361 -0.01347 0.120733 0.014973 0.191075 0.023697 0.003817 -0.058672020/4/6 0.052567 0.02299 0.074351 0.067968 -0.0339 1065.43 2663.68 88 25051 2561 1124 45.24 22011 0.024562 0.016369 0.198049 0.131989 0.050231 0.115361 0.014307 0.123725 0.015344 0.002337 0.0488392020/4/7 -0.009373 -0.09531 0.402947 -0.0016 0.031762 1055.49 2659.41 80 37482 2390 2070 46.7 22012 0.01865 0.009234 0.150376 0.074458 0.019838 0.131989 0.016369 0.198049 0.024562 -0.02921 0.0966852020/4/8 0.041196 -0.09157 -0.37477 0.033489 -0.07444 1099.88 2749.98 73 25767 2489 1210 43.35 22013 0.016829 0.009401 0.135699 0.075799 0.065174 0.074458 0.009234 0.150376 0.01865 -0.02398 -0.184182020/4/9 0.005558 -0.05635 0.189559 0.014383 -0.03953 1106.01 2789.82 69 31145 1752 1882 41.67 22014 0.017515 0.014727 0.141227 0.118748 -0.01084 0.075799 0.009401 0.135699 0.016829 0.016399 0.2968162020/4/13 -0.009868 0.117783 0.057028 -0.01016 -0.01207 1095.15 2761.63 63 27457 2086 1514 41.17 22018 0.014944 0.009671 0.120495 0.077982 -0.00409 0.118748 0.014727 0.141227 0.017515 -0.00578 -0.40152020/4/14 0.03252 -0.08269 0.12927 0.030115 -0.08646 1131.35 2846.06 58 31246 4681 1536 37.76 22019 0.009842 0.008294 0.079358 0.066879 -0.00465 0.077982 0.009671 0.120495 0.014944 0.037172 0.054082020/4/15 -0.005255 -0.03509 -0.14936 -0.02228 0.078412 1125.42 2783.36 56 26911 1564 2527 40.84 22020 0.012747 0.009089 0.102783 0.07329 -0.04787 0.066879 0.008294 0.079358 0.009842 0.042614 -0.067622020/4/16 0.021736 0.0177 0.293952 0.0058 -0.01804 1150.15 2799.55 57 36107 13860 6581 40.11 22021 0.018986 0.00903 0.153088 0.072812 -0.04055 0.07329 0.009089 0.102783 0.012747 0.062288 -0.004512020/4/17 0.020465 -0.05407 -0.2215 0.026441 -0.0501 1173.93 2874.56 54 28933 5105 1998 38.15 22022 0.019974 0.009542 0.161052 0.076937 0.099242 0.072812 0.00903 0.153088 0.018986 -0.07878 0.1116992020/4/20 -0.007816 0.058269 -0.19561 -0.01804 0.138793 1164.79 2823.16 53 25587 2825 1477 43.83 22025 0.013455 0.007468 0.108492 0.060215 -0.0335 0.076937 0.009542 0.161052 0.019974 0.025679 -0.103972020/4/21 -0.031891 -0.03847 0.057744 -0.03116 0.035414 1128.23 2736.56 51 27108 1129 1821 45.41 22026 0.012495 0.006105 0.100749 0.049224 -0.01692 0.060215 0.007468 0.108492 0.013455 -0.01498 -0.028042020/4/22 0.015898 0.019418 0.171982 0.022671 -0.07854 1146.31 2799.31 52 32195 10563 2849 41.98 22027 0.013875 0.011789 0.111881 0.095061 0.035189 0.049224 0.006105 0.100749 0.012495 -0.01929 -0.005172020/4/23 0.004804 -0.05942 -0.29155 -0.00054 -0.0144 1151.83 2797.8 49 24053 1077 2344 41.38 22028 0.013393 0.013247 0.10799 0.106817 0.029683 0.095061 0.011789 0.111881 0.013875 -0.02488 0.1310122020/4/24 0.014309 -0.08516 0.447143 0.013822 -0.14123 1168.43 2836.74 45 37615 1872 2559 35.93 22029 0.009008 0.007435 0.072635 0.05995 0.002081 0.106817 0.013247 0.10799 0.013393 0.012228 -0.068672020/4/27 0.01306 0.178248 -0.16503 0.014607 -0.07632 1183.79 2878.48 49 27020 619 1160 33.29 22032 0.014118 0.007256 0.113836 0.058506 0.020802 0.05995 0.007435 0.072635 0.009008 -0.00774 -0.034112020/4/28 -0.021526 -0.06318 -0.10895 -0.00526 0.008376 1158.58 2863.39 46 24231 20638 1508 33.57 22033 0.014646 0.008739 0.118094 0.070463 0.021683 0.058506 0.007256 0.113836 0.014118 -0.04321 0.0881432020/4/29 0.00737 -0.04445 0.001608 0.026237 -0.07225 1167.15 2939.51 44 24270 3679 2351 31.23 22034 0.022337 0.017707 0.180106 0.142773 0.07094 0.070463 0.008739 0.118094 0.014646 -0.06357 0.154422020/4/30 -0.004396 -0.07062 0.189097 -0.00926 0.089383 1162.03 2912.43 41 29322 4375 2431 34.15 22035 0.017344 0.00799 0.13985 0.064424 -0.02263 0.142773 0.017707 0.180106 0.022337 0.018235 -0.014762020/5/1 -0.020993 -0.02469 0.134281 -0.02846 0.085277 1137.89 2830.71 40 33536 8616 2257 37.19 22036 0.01446 0.008811 0.116597 0.071044 -0.06184 0.064424 0.00799 0.13985 0.017344 0.04085 -0.316542020/5/4 0.000729 0.075986 -0.02893 0.004241 -0.03336 1138.72 2842.74 41 28477 4761 1167 35.97 22039 0.011673 0.009062 0.094125 0.073071 0.036423 0.071044 0.008811 0.116597 0.01446 -0.03569 -0.006342020/5/5 0.021279 -0.02469 -0.25018 0.009 -0.06786 1163.21 2868.44 40 22174 9398 1272 33.61 22040 0.012088 0.006756 0.097467 0.054473 0.002617 0.073071 0.009062 0.094125 0.011673 0.018661 0.0825522020/5/6 -0.009875 -0.02532 0.152384 -0.007 0.01506 1151.78 2848.42 39 25824 13083 2407 34.12 22041 0.014753 0.007937 0.118958 0.063999 -0.02667 0.054473 0.006756 0.097467 0.012088 0.016792 -0.053592020/5/7 -0.000452 0 -0.01793 0.011439 -0.0818 1151.26 2881.19 39 25365 11974 2500 31.44 22042 0.015172 0.00834 0.122332 0.067248 0.024439 0.063999 0.007937 0.118958 0.014753 -0.02489 0.0604022020/5/8 0.00538 -0.10821 0.123353 0.016731 -0.11659 1157.47 2929.8 35 28695 4125 2117 27.98 22043 0.012352 0.007903 0.099601 0.063721 0.042484 0.067248 0.00834 0.122332 0.015172 -0.0371 -0.061382020/5/11 0.016877 0.167054 -0.21592 0.000133 -0.01476 1177.17 2930.19 39 20344 18264 745 27.57 22046 0.016351 0.006242 0.131843 0.05033 -0.01701 0.063721 0.007903 0.099601 0.012352 0.033882 -0.010312020/5/12 -0.015021 -0.02598 -0.1037 -0.02071 0.180991 1159.62 2870.12 38 18340 5981 1172 33.04 22047 0.012754 0.006432 0.102841 0.051861 -0.02392 0.05033 0.006242 0.131843 0.016351 0.008902 0.0606112020/5/13 -0.011056 0 0.220523 -0.01762 0.065597 1146.87 2820 38 22865 36317 1546 35.28 22048 0.012765 0.009436 0.102924 0.076083 -0.04485 0.051861 0.006432 0.102841 0.012754 0.033798 0.1845832020/5/14 0.010685 -0.02667 -0.0283 0.011459 -0.0787 1159.19 2852.5 37 22227 11772 1770 32.61 22049 0.011984 0.004695 0.096628 0.037856 0.009382 0.076083 0.009436 0.102924 0.012765 0.001303 -0.085112020/5/15 0.007255 -0.08456 0.21386 0.003919 -0.02233 1167.63 2863.7 34 27527 7621 1691 31.89 22050 0.011149 0.006467 0.089901 0.052144 -0.00279 0.037856 0.004695 0.096628 0.011984 0.010042 -0.029662020/5/18 0.009334 0.117783 -0.00385 0.031015 -0.08471 1178.58 2953.91 36 22293 7214 919 29.3 22053 0.024622 0.01104 0.198534 0.089019 0.072788 0.052144 0.006467 0.089901 0.011149 -0.06345 0.1501382020/5/19 -0.012147 -0.05716 -0.08059 -0.01054 0.041122 1164.35 2922.94 34 20567 12132 1011 30.53 22054 0.010013 0.007242 0.080741 0.058392 -0.02935 0.089019 0.01104 0.198534 0.024622 0.0172 -0.247422020/5/20 0.001227 -0.02985 -0.07799 0.016514 -0.08686 1165.78 2971.61 33 19024 2309 1489 27.99 22055 0.015993 0.006603 0.128955 0.053244 0.037475 0.058392 0.007242 0.080741 0.010013 -0.03625 0.0047462020/5/21 -0.008148 0 0.231936 -0.0078 0.053559 1156.32 2948.51 33 23990 9746 1460 29.53 22056 0.010206 0.005183 0.08229 0.041795 -0.01495 0.053244 0.006603 0.128955 0.015993 0.006798 -0.005232020/5/22 0.001892 -0.12921 0.118903 0.002351 -0.0475 1158.51 2955.45 29 27019 11963 1364 28.16 22057 0.010353 0.003019 0.083479 0.024345 -0.00669 0.041795 0.005183 0.08229 0.010206 0.008584 -0.228382020/5/26 -0.001935 0.129212 -0.06267 0.012214 -0.00534 1156.27 2991.77 33 19807 13923 528 28.01 22061 0.01842 0.005902 0.148528 0.047592 0.028657 0.024345 0.003019 0.083479 0.010353 -0.03059 0.3898032020/5/27 0.010445 -0.06252 -0.01224 0.014718 -0.01402 1168.41 3036.13 31 19566 14605 777 27.62 22062 0.015091 0.005782 0.121683 0.04662 0.011536 0.047592 0.005902 0.148528 0.01842 -0.00109 0.0875652020/5/28 0.012503 -0.06669 0.032186 -0.00211 0.034517 1183.11 3029.73 29 20206 9983 1555 28.59 22063 0.012699 0.006825 0.102392 0.055029 -0.02952 0.04662 0.005782 0.121683 0.015091 0.042024 -0.16492020/5/29 0.012624 -0.1092 0.106246 0.004801 -0.03851 1198.14 3044.31 26 22471 8857 1176 27.51 22064 0.013213 0.009886 0.106543 0.079714 -0.00154 0.055029 0.006825 0.102392 0.012699 0.014166 0.297562 Long horizon hclg date hccssd laggedhccssdsplg vollg vixlg elg ecssd laggedecssdgolg inlg laggedhccsadhccsad laggedecsadecsad helg newin dnewin-0.00623 0.065067 0.047178 -0.00382 0.107147 0.078865 -0.00165 0.039737 0.039737 0 0 0.00521 0.007185 0.004388 0.004341 -0.00458 0 00.000316 0.06075 0.065067 -0.01057 -0.02733 0.093205 -0.01268 0.03931 0.03931 0 0 0.007185 0.006708 0.004341 0.00325 0.012996 0 0-0.03318 0.117001 0.06075 -0.03409 0.216737 0.382167 -0.04853 0.029432 0.029432 0.405465 0 0.006708 0.01292 0.00325 0.005219 0.015355 19 19-0.02995 0.082479 0.117001 -0.03075 0.143723 0.106758 -0.04436 0.047263 0.047263 0 0 0.01292 0.009108 0.005219 0.003036 0.014411 4 -15-0.00103 0.075183 0.082479 -0.00379 -0.02049 -0.01047 -0.03013 0.027492 0.027492 0.510826 -1.55814 0.009108 0.008302 0.003036 0.005014 0.029105 3 -1-0.03388 0.107957 0.075183 -0.04517 0.253521 0.35129 -0.05627 0.045403 0.045403 0.182322 -0.28768 0.008302 0.011921 0.005014 0.007678 0.022389 0 -3-0.01419 0.105141 0.107957 -0.00827 0.193269 0.02397 0.01239 0.069536 0.069536 0.154151 0 0.011921 0.01161 0.007678 0.007436 -0.02658 20 200.04713 0.095188 0.105141 0.045011 -0.29495 -0.18247 0.029118 0.067337 0.067337 0.693147 1.38629 0.01161 0.010511 0.007436 0.004869 0.018012 17 -3-0.02577 0.092042 0.095188 -0.02851 -0.00321 0.096887 -0.03171 0.044093 0.044093 0 -0.16252 0.010511 0.010164 0.004869 0.004839 0.005939 20 30.056496 0.117056 0.092042 0.041336 -0.23288 -0.14062 0.021967 0.043827 0.043827 0.09531 0.162519 0.010164 0.012926 0.004839 0.005059 0.034529 35 15-0.02424 0.097205 0.117056 -0.03451 0.101882 0.213911 -0.03682 0.045816 0.045816 0.167054 0.559616 0.012926 0.010734 0.005059 0.004001 0.012572 72 37-0.0052 0.091892 0.097205 -0.0172 0.161401 0.056906 -0.05777 0.036237 0.036237 0.207639 0.721318 0.010734 0.010147 0.004001 0.015661 0.052575 127 55-0.05328 0.119227 0.091892 -0.07901 0.25118 0.261226 -0.22417 0.141829 0.141829 0.538997 0.171358 0.010147 0.013165 0.015661 0.053043 0.170892 145 180.034099 0.114052 0.119227 0.048215 -0.0981 -0.14096 0.048743 0.480364 0.480364 0.117783 0.132547 0.013165 0.012594 0.053043 0.015636 -0.01464 287 142-0.03988 0.142106 0.114052 -0.0501 -0.03489 0.13062 -0.05615 0.141604 0.141604 0.315081 0.682748 0.012594 0.015692 0.015636 0.015328 0.016274 319 32-0.077 0.183329 0.142106 -0.09995 0.18011 0.336605 -0.1312 0.138814 0.138814 0.516216 0.105709 0.015692 0.020244 0.015328 0.017939 0.054203 509 1900.067224 0.195688 0.183329 0.088808 -0.06682 -0.26623 0.08472 0.162457 0.162457 0.077558 0.467257 0.020244 0.021608 0.017939 0.012981 -0.0175 787 278-0.10527 0.297931 0.195688 -0.12765 -0.05951 0.357591 -0.14649 0.117557 0.117557 0.364222 0.11145 0.021608 0.032898 0.012981 0.01548 0.041218 1291 5040.060676 0.269636 0.297931 0.058226 0.071525 -0.08555 0.007219 0.14019 0.14019 -0.05407 0.494944 0.032898 0.029774 0.01548 0.021297 0.053457 1463 172-0.03456 0.276229 0.269636 -0.05322 0.046435 0.007088 -0.1541 0.192866 0.192866 0.064539 0.125072 0.029774 0.030502 0.021297 0.028987 0.119543 3989 2526-0.01884 0.310615 0.276229 0.004697 -0.09696 -0.05997 0.065288 0.262504 0.262504 -0.01047 1.00305 0.030502 0.034299 0.028987 0.0225 -0.08413 3862 -127-0.04162 0.230319 0.310615 -0.04433 0.12942 -0.08641 0.009585 0.203757 0.203757 -0.01058 -0.03236 0.034299 0.025433 0.0225 0.014072 -0.0512 12072 8210-0.05103 0.209707 0.230319 -0.02973 -0.2004 -0.06976 -0.06884 0.127433 0.127433 0.117783 0.477721 0.025433 0.023156 0.014072 0.016767 0.017805 7267 -48050.073138 0.227665 0.209707 0.089683 0.019422 0.001298 0.151108 0.151844 0.151844 -0.08426 -0.50755 0.023156 0.025139 0.016767 0.015037 -0.07797 8781 15140.012577 0.245472 0.227665 0.011469 0.093331 0.036304 0.043948 0.136177 0.136177 -0.01105 0.189247 0.025139 0.027106 0.015037 0.01335 -0.03137 13966 51850.067476 0.143948 0.245472 0.060544 -0.06643 -0.04723 0.060576 0.120902 0.120902 0.085158 0.464036 0.027106 0.015895 0.01335 0.009024 0.0069 16815 2849-0.02442 0.123781 0.143948 -0.03427 -0.22447 0.071787 -0.07182 0.081719 0.081719 0.020203 0.185646 0.015895 0.013668 0.009024 0.013304 0.0474 18856 20410.045666 0.129719 0.123781 0.032967 -0.07509 -0.13821 0.010289 0.120485 0.120485 0.110001 -0.0593 0.013668 0.014324 0.013304 0.012926 0.035377 22040 3184-0.00394 0.109552 0.129719 -0.01614 0.133711 -0.06403 0.0162 0.117055 0.117055 -0.02105 0.156028 0.014324 0.012097 0.012926 0.012183 -0.02014 23989 1949-0.03938 0.172056 0.109552 -0.04515 -0.09922 0.063674 -0.04748 0.110332 0.110332 -0.02151 0.084736 0.012097 0.018999 0.012183 0.00847 0.008109 26969 29800.027474 0.169562 0.172056 0.022573 0.081815 -0.11404 0.086851 0.076704 0.076704 0.04256 0.117093 0.018999 0.018724 0.00847 0.011831 -0.05938 38734 11765-0.00966 0.109795 0.169562 -0.01525 -0.05867 -0.08418 -0.01347 0.10714 0.10714 -0.04256 0.36203 0.018724 0.012124 0.011831 0.011304 0.003816 25051 -136830.052567 0.175751 0.109795 0.067968 0.048839 -0.0339 0.050231 0.102373 0.102373 0.083881 0.074351 0.012124 0.019407 0.011304 0.012934 0.002336 37482 12431-0.00937 0.133446 0.175751 -0.0016 0.096685 0.031762 0.019838 0.117129 0.117129 -0.1092 0.402947 0.019407 0.014735 0.012934 0.007296 -0.02921 25767 -117150.041196 0.120421 0.133446 0.033489 -0.18418 -0.07444 0.065174 0.066075 0.066075 -0.06625 -0.37477 0.014735 0.013297 0.007296 0.007428 -0.02398 31145 53780.005558 0.125327 0.120421 0.014383 0.296816 -0.03953 -0.01084 0.067265 0.067265 -0.04196 0.189559 0.013297 0.013839 0.007428 0.011636 0.016399 37770 6625-0.00987 0.106929 0.125327 -0.01016 -0.4015 -0.01207 -0.00409 0.105378 0.105378 0.13815 0.057028 0.013839 0.011807 0.011636 0.007642 -0.00578 27457 -103130.03252 0.070424 0.106929 0.030115 0.05408 -0.08646 -0.00465 0.069202 0.069202 -0.01626 0.12927 0.011807 0.007776 0.007642 0.006554 0.037172 31246 3789-0.00526 0.091211 0.070424 -0.02228 -0.06762 0.078412 -0.04787 0.05935 0.05935 -0.06782 -0.14936 0.007776 0.010072 0.006554 0.007182 0.042615 26911 -43350.021736 0.135852 0.091211 0.0058 -0.00451 -0.01804 -0.04055 0.065039 0.065039 0.017392 0.293952 0.010072 0.015001 0.007182 0.007135 0.062288 36107 91960.020465 0.142919 0.135852 0.026441 0.111699 -0.0501 0.099242 0.064614 0.064614 -0.03509 -0.2215 0.015001 0.015782 0.007135 0.007539 -0.07878 28933 -7174-0.00782 0.096277 0.142919 -0.01804 -0.10397 0.138793 -0.0335 0.068275 0.068275 0.059423 -0.19561 0.015782 0.010631 0.007539 0.0059 0.025679 25587 -3346-0.03189 0.089405 0.096277 -0.03116 -0.02804 0.035414 -0.01692 0.053435 0.053435 -0.01942 0.057744 0.010631 0.009872 0.0059 0.004823 -0.01498 27108 15210.015898 0.099285 0.089405 0.022671 -0.00517 -0.07854 0.035189 0.043682 0.043682 -0.0198 0.171982 0.009872 0.010963 0.004823 0.009315 -0.01929 32195 50870.004804 0.095832 0.099285 -0.00054 0.131012 -0.0144 0.029683 0.084358 0.084358 -0.04082 -0.29155 0.010963 0.010582 0.009315 0.010467 -0.02488 24053 -81420.014309 0.064458 0.095832 0.013822 -0.06867 -0.14123 0.002081 0.094791 0.094791 -0.06454 0.447143 0.010582 0.007118 0.010467 0.005875 0.012228 37615 135620.01306 0.10102 0.064458 0.014607 -0.03411 -0.07632 0.020802 0.0532 0.0532 0.139762 -0.16503 0.007118 0.011155 0.005875 0.005733 -0.00774 27020 -10595-0.02153 0.104798 0.10102 -0.00526 0.088143 0.008376 0.021683 0.051919 0.051919 -0.02198 -0.10895 0.011155 0.011572 0.005733 0.006905 -0.04321 24231 -27890.00737 0.159829 0.104798 0.026237 0.15442 -0.07225 0.07094 0.06253 0.06253 -0.02247 0.001608 0.011572 0.017649 0.006905 0.01399 -0.06357 24270 39-0.0044 0.124104 0.159829 -0.00926 -0.01476 0.089383 -0.02263 0.126699 0.126699 -0.07062 0.189097 0.017649 0.013704 0.01399 0.006313 0.018236 29322 5052-0.02099 0.103469 0.124104 -0.02846 -0.31654 0.085277 -0.06184 0.057171 0.057171 -0.02469 0.134281 0.013704 0.011425 0.006313 0.006962 0.040849 33536 42140.000729 0.083528 0.103469 0.004241 -0.00634 -0.03336 0.036423 0.063045 0.063045 0.105361 -0.02893 0.011425 0.009223 0.006962 0.00716 -0.03569 28477 -50590.021279 0.086494 0.083528 0.009 0.082552 -0.06786 0.002617 0.064844 0.064844 0 -0.25018 0.009223 0.009551 0.00716 0.005338 0.018662 22174 -6303-0.00988 0.105564 0.086494 -0.007 -0.05359 0.01506 -0.02667 0.04834 0.04834 0 0.152384 0.009551 0.011657 0.005338 0.006271 0.016791 25824 3650-0.00045 0.108559 0.105564 0.011439 0.060402 -0.0818 0.024439 0.056793 0.056793 0 -0.01793 0.011657 0.011987 0.006271 0.00659 -0.02489 25365 -4590.00538 0.088387 0.108559 0.016731 -0.06138 -0.11659 0.042484 0.059676 0.059676 0 0.123353 0.011987 0.00976 0.00659 0.006244 -0.0371 28695 33300.016877 0.116999 0.088387 0.000133 -0.01031 -0.01476 -0.01701 0.056547 0.056547 0.047628 -0.21592 0.00976 0.012919 0.006244 0.004932 0.033883 20344 -8351-0.01502 0.091262 0.116999 -0.02071 0.060611 0.180991 -0.02392 0.044664 0.044664 -0.07232 -0.1037 0.012919 0.010077 0.004932 0.005082 0.008901 18340 -2004-0.01106 0.091336 0.091262 -0.01762 0.184583 0.065597 -0.04485 0.046022 0.046022 0 0.220523 0.010077 0.010086 0.005082 0.007455 0.033797 22865 45250.010685 0.085749 0.091336 0.011459 -0.08511 -0.0787 0.009382 0.067517 0.067517 0 -0.0283 0.010086 0.009469 0.007455 0.00371 0.001303 22227 -6380.007255 0.079779 0.085749 0.003919 -0.02966 -0.02233 -0.00279 0.033594 0.033594 -0.02532 0.21386 0.009469 0.008809 0.00371 0.00511 0.010042 27527 53000.009334 0.176181 0.079779 0.031015 0.150138 -0.08471 0.072788 0.046273 0.046273 0.11441 -0.00385 0.008809 0.019454 0.00511 0.008723 -0.06345 22293 -5234-0.01215 0.07165 0.176181 -0.01054 -0.24742 0.041122 -0.02935 0.078997 0.078997 -0.05557 -0.08059 0.019454 0.007912 0.008723 0.005722 0.0172 20567 -17260.001227 0.114436 0.07165 0.016514 0.004746 -0.08686 0.037475 0.051817 0.051817 0.028171 -0.07799 0.007912 0.012636 0.005722 0.005217 -0.03625 19024 -1543-0.00815 0.073025 0.114436 -0.0078 -0.00523 0.053559 -0.01495 0.047249 0.047249 0 0.231936 0.012636 0.008064 0.005217 0.004096 0.006798 23990 49660.001892 0.07408 0.073025 0.002351 -0.22838 -0.0475 -0.00669 0.03709 0.03709 -0.08701 0.118903 0.008064 0.00818 0.004096 0.002386 0.008584 27019 3029-0.00194 0.131805 0.07408 0.012214 0.389803 -0.00534 0.028657 0.021604 0.021604 0.125163 -0.06267 0.00818 0.014554 0.002386 0.004664 -0.03059 19807 -72120.010445 0.107983 0.131805 0.014718 0.087565 -0.01402 0.011536 0.042234 0.042234 -0.06063 -0.01224 0.014554 0.011924 0.004664 0.004568 -0.00109 19566 -2410.012503 0.090864 0.107983 -0.00211 -0.1649 0.034517 -0.02952 0.041371 0.041371 0 0.032186 0.011924 0.010033 0.004568 0.005392 0.042025 20206 6400.012624 0.094548 0.090864 0.004801 0.297562 -0.03851 -0.00154 0.048834 0.048834 -0.13353 0.106246 0.010033 0.01044 0.005392 0.007811 0.014166 22471 2265-0.01011 0.074577 0.094548 0.003744 -0.44257 0.025836 0.016699 0.07074 0.07074 0.122602 -0.14427 0.01044 0.008235 0.007811 0.007541 -0.02681 19891 -25800.00606 0.071533 0.074577 0.008177 0.104311 -0.05049 0.026197 0.068294 0.068294 0 0.091413 0.008235 0.007899 0.007541 0.004124 -0.02014 21795 1904-0.002 0.079436 0.071533 0.013557 0.143818 -0.04496 0.030034 0.03735 0.03735 0 -0.03697 0.007899 0.008772 0.004124 0.004604 -0.03203 21004 -791-0.00809 0.082183 0.079436 -0.00337 0.070666 0.005829 -0.00153 0.041693 0.041693 0.143101 0.068714 0.008772 0.009075 0.004604 0.004523 -0.00656 22498 14940.01643 0.139665 0.082183 0.025874 0.293122 -0.05127 0.071911 0.040961 0.040961 -0.0339 -0.05505 0.009075 0.015422 0.004523 0.012072 -0.05548 21293 -12050.006367 0.08643 0.139665 0.01197 -0.02113 0.051273 0.0423 0.109328 0.109328 0.207639 -0.15294 0.015422 0.009544 0.012072 0.011369 -0.03593 18190 -3103-0.01087 0.091128 0.08643 -0.00783 -0.27909 0.065966 -0.03655 0.102961 0.102961 0.089612 0.056535 0.009544 0.010063 0.011369 0.00655 0.025678 19248 1058-0.00138 0.124281 0.091128 -0.00533 0.029063 0 -0.05045 0.059313 0.059313 0 -0.00735 0.010063 0.013723 0.00655 0.006206 0.049064 19107 -141-0.05791 0.101171 0.124281 -0.06075 0.065963 0.391709 -0.0993 0.056201 0.056201 0 0.094087 0.013723 0.011172 0.006206 0.009404 0.04139 20992 18850.006934 0.075546 0.101171 0.012976 -0.1852 -0.12242 0.026717 0.085159 0.085159 0.028171 0.133621 0.011172 0.008342 0.009404 0.006415 -0.01978 23993 3001