Why Does Return Volatility Differ in
Chinese Stock Markets?
Dongwei Su∗
Department of Economics, University of Akron Akron, OH 44325, USA
[email protected] Belton M. Fleisher
Department of Economics, The Ohio State University Columbus, OH 43210, USA
January 25, 1998 Abstract
We estimate a dynamic model under Anderson’s Modified Mixture of Distribution Hypothesis (MMDH) to explore the underlying causes of the volatility differences be-tween China’s domestic A shares and foreign B shares. We find evidence that some of the greater return volatility for A-shares is due to a substantially larger number of investors leading to a higher probability of trading on a given “news” flow.
Key words: Stochastic volatility; Trading volume; Mixture of distribution; Market
seg-mentation; China
JEL classification: C52; G10; O16
∗We would like to acknowledge Torben Anderson, Yue Fang, Pok-sang Lam, Masao Ogaki, Steve
Yamarik, Qiang Zhang and seminar participants at a session “Financial Markets in China” during the 1998 ASSA meetings in Chicago for their valuable comments.
1
Introduction
In this paper, we attempt to resolve an intriguing problem in Chinese stock markets: Why is return volatility for domestic A-shares so much higher than for foreign B-shares, even though the two share categories are entitled to identical rights and dividends within the same company?
Chinese stock markets are segmented in the sense that A shares are available only to Chinese citizens and B shares can only be purchased by foreign investors. Both types of shares are traded in the Shanghai and Shenzhen exchanges, but companies are not cross-listed. Bailey (1994) provides early evidence that B shares are sold and traded at various discounts relative to their A-share counterparts. Su and Fleisher (1997) find that the volatility of stock-market return is much higher for A shares than for B shares. In the sample used in the current paper, the unweighted means of daily returns were 0.0303% and 0.0516% while the standard deviations were 6.0146% and 3.8916%, for A-and B-shares, respectively.
To explore the sources of volatility differences in A- and B-share markets, we estimate a model under the Modified Mixture of Distribution Hypothesis (MMDH, Andersen, 1996) in which stock returns and trading volumes are assumed to be contemporaneously dependent on an underlying mixing variable representing the non-uniform intensity of information flow (relative to an unobserved benchmark level) over time. Since we do not observe the actual level of the latent information flow, we assume that the unob-served benchmark information flow to A-share investors is no less than that to B-shares investors. To model positive autocorrelation in news arrival, we allow the latent in-formation flow to follow a stochastic autoregressive process. We estimate the dynamic system relating stock returns and trading volume using Generalized Method of Moments (GMM) and obtain parameter estimates characterizing the distribution of the unobserv-able daily information arrival for 24 companies that issue both A and B shares over the period August 6, 1993 through September 15, 1997.
In the next section, we briefly discuss the MMDH. In Section 3, we present and interpret our empirical results. Our findings are summarized in the conclusion.
2
Empirical Model and Estimation
Anderson’s MMDH can be modeled as
Rt = µ + Zt
q
Kt (1)
ˆ
Vt|Kt∼c · P o(m0+ m1Kt) (2)
where Rt is the stock return on day t, Zt is a standard normal random variable, Kt is
a mixing variable, usually interpreted as the unobserved flow of underlying information pertaining to the future dividends and/or the liquidation value of a particular stock, ˆVtis
the detrended, stationary trading volume series that is conditionally Poisson distributed,
m0 is the daily arrival intensity of noise trading that is independent of the information
flow, and m1 is the number of informed investors multiplied by the probability that
an informed investor will trade given the benchmark news arrivals on that day. The parameter c is a constant of proportionality arising from the detrending process. In equations (1) and (2), the volatility of daily returns is the latent information flow itself. For a Chinese company that issues both A and B shares, if E(KtA) and the estimate of
cmA1 are larger than E(KtB) and cmB1, respectively, then we can take this as evidence that a greater magnitude of news arrival, operating through trading volume, explains the company’s “excess” A-share volatility.
To model a dynamic process governing information arrivals, Ktis assumed to follow a
lognormal stationary stochastic autoregressive process that displays positive conditional dependency:
lnqKt = α + β ln
q
Kt−1+ γut, and Kt≥0 (3)
where 0 ≤ β < 1, α > 0, γ > 0, and ut∼i.i.d.N(0, 1).
It follows from equation (3) that E(ln√Kt) = α/(1 − β), V ar(ln
√ Kt) = γ/(1 − β2) and Cov(ln√Kt, ln q Kt−j) = βjV ar(ln √ Kt) = (βjγ)/(1 − β2). The unconditional
moments for Kt are:
E( q Ktn) = exp " nE(ln q Kt) + n2 2 V ar(ln q Kt) # = exp " nα 1 − β + n2γ 2(1 − β2) # , (4)
EµqKn t · q Km t−j ¶ = EµqKn t ¶ ·E³qKm t−j ´ exp · mnCov µ ln q Kt, ln q Kt−j ¶¸ = exp " (n + m)α 1 − β + (n2+ m2+ 2mnβj)γ 2(1 − β2) # , (5)
where n and m can be any positive integer.
Our dynamic system for stock returns and trading volume consists of equations (1)-(3). The following 26 unconditional moments are exploited to estimate the seven unknown coefficients (µ, α, β, γ, c, m0, m1) using the GMM developed by Hansen (1982)1:
E(Rt) = µ (6) E( ˆVt) = cm0+ cm1E(Kt) = ¯V (7) V ar(Rt) = E(Kt) (8) V ar( ˆVt) = c2m21V ar(Kt) (9) E(Rt, ˆVt) = µ(cm0+ cm1E(Kt)) = µ ¯V (10) E(|Rt−µ|) = s 2 πE( q Kt) (11)
E[(Rt−µ1)2Vˆt] = cm0E(Kt) + cm1E(Kt2) (12)
E(|Rt−µ| ˆVt) = cm0 s 2 πE( q Kt) + cm1 s 2 πE( q K3 t) (13) E[(Rt−µ)2(Rt−j−µ)2] = 2 πE(Kt, Kt−j) (14) E[( ˆVt− ¯V )( ˆVt−j− ¯V )] = c21m 2 1Cov(Kt, Kt−j) (15) E(|Rt−µ||Rt−j−µ|) = 2 πE( q Kt, q Kt−j) (16) where j = 1, · · · , 6.
1Since the moment conditions are highly nonlinear in the unknown parameters, we choose lower
order moments for Kt to avoid computation complications. It should be noted, however, that GMM
is subject to the appropriate choice of moment conditions. GMM estimators are consistent but can be less efficient than Simulated Maximum Likelihood as discussed in Liesenfeld (1997, 1998).
3
Empirical Results
The raw data consist of daily closing prices and trading volume for all 24 companies represented by both A- and B- share issues for the period August 6, 1993 through September 25, 1997 for a total of 1021 observations. Cum-dividend returns are computed using ln(Pt+ Dt) − ln Pt−1. We follow Gallant, Rossi and Tauchen (1992) in removing
trend and other systematic calendar effects from the volume data.2
We estimate our dynamic system of stock returns and trading volume by the GMM.3
Table 1 presents the parameter estimates and standard errors for µ, α, β, γ, c, m0, m1
for all 24 companies. Using Hansen’s J -statistics for overidentifying restrictions, we find that the MMDH cannot be rejected for 21 out of 24 Chinese companies. Table 2 presents estimates for for cm0 and cm1, as well as the mean, variance and kurtosis for the mixing
variable Kt for 21 companies. As shown in the table, E(Kt) is uniformly higher for
A shares than for B shares, ranging from 1.9187 to 4.7095 with an average of 3.0810 for A shares, and from 1.1685 to 2.5890 with an average of 2.0615 for B shares. These estimates imply that daily news arrivals have been approximately 33.1% larger across all 21 A shares than across B shares. The parameter cm0, representing the average fraction
of the daily trading volume unrelated to news arrival (noise trading) ranges from 0.1699 to 0.3774 with an average of 0.2574 for A shares and from 0.23978 to 0.5854 with an average of 0.3873 for B shares. This implies, of course, that the proportional importance of informed trading volume is greater for A shares. The parameter cm1, the proportion
of informed trading volume due to news arrival, ranges from 0.161 to 0.5914 with an average of 0.4768 for A shares and from 0.1968 to 0.5034 with an average of 0.3331 for B shares, offering further support to the role of information flows in determining A- and
2In particular, we use the following set of dummy and time-trend variables in the adjustment
re-gression: (1) Day-of-the-week dummies (Tuesday through Friday); (2) Weekend and holiday dummies for the number of non-trading days preceding the current trading day; (3) Dummy variables for each month (January, and March through December); (4) Dummy variables for each year (1994 to 1997); (5) A time trend variable = 1, · · · , 1021.
We first regress the logarithm of trading volume (ln Vt) on the above set of adjustment variables and
obtain the trading volume that is assumed to be due to factors not systematically related to news or information arrival ( dln Vt). Then we divide ln Vt by dln Vt, the “non-constant noise” component and
obtain a detrended volume series ˆVtwhich has mean 1.
3We use a Gauss program written and made publicly available by Hansen, Heaton and Ogaki for
B-share relative volatility.4
It is irresistible to ask why, if rights and dividends are identical across A- and B-shares, information relevant to domestic and foreign investors is not also identically distributed. The answer, we believe, lies in the proximity of domestic investors to their information sources. Moreover, the larger number of and, presumably, higher geographical density, of domestic investors intuitively leads to a more rapid transmission of news and, likely, a greater affect on trading volume, consistent with our results. We should note, though, that the MMDH’s definition of news is value-free, in the sense that “truth” and “gossip” are indistinguishable without information extraneous to the model as specified above. “Information is what information does,” and anything leading to non-noise trading is defined to be “information.”
In an attempt to gain some insight into the nature of the difference in information flows to the A- and B-share markets, we maintain the following hypotheses:
(1) News observable by both A- and B-share investors (or publicly available infor-mation) is positively correlated with the standard deviation of profit-per-share over the sample period across firms. In other words, the standard deviation of profit-per-share over the sample period for a firm is a proxy for the benchmark information flow to that firm.
(2) News observable to informed A-share investors but unobservable to B-share in-vestors (“gossip” and “insider” information available only to domestic Chinese) is positively correlated with information observable to all investors (e.g., standard deviation of profit-per-share). The rationale for this maintained hypothesis is that if a firm’s time-series of profit-per-share is flat, nobody will find it worthwhile thinking, talking and gossiping about such a firm. But if there is a lot of actual and potential changes in a firm’s future earnings, then it may be worthwhile for investors to acquire information and gossip about the firm.
(3) The probability of trade, given a certain amount of information arrival, is positively
4The estimates for persistence in return volatility (α + β) are large and statistically significantly
pos-itive across companies. This is consistent with the findings in Su and Fleisher (1997), who documented a GARCH effect in the Chinese stock markets using A- and B-share market indices. The persistence in return volatility ranges from 0.5807 to 0.9357 with an average of 0.7749 for A shares and from 0.4034 to 0.7713 with an average of 0.5503 for B shares.
related to the number of investors. This follows from the market microstructure theory described in Anderson (1996).
(4) Noise trading, or liquidity trading, is uncorrelated with any proxy for information flow.
(5) The proportion of noise traders is uncorrelated with the number of investors. Based on the above assumptions, we relate the average fraction of daily volume associated with information arrivals (cm1) and the expected number of trades on a day
(m1) to the following variables: the standard deviation of profit-per-share from August
1993 to September 1997 (ST DP ROFij, i = 1, 2, · · · , 21, j ∈ {A-share, B-share}), a dummy variable that takes value 1 for A shares and 0 for B shares (Dij), and the number of j-share investors for firm i (IN V STij):
cmj1,i = 0.2614 + 0.5572ST DP ROFij + 0.2136Dij
(0.0441) (0.3050) (0.0624)
−0.5436(Dji ·ST DP ROFij) + ξij
(0.4313) R¯2 = 0.3845 (17)
mj1,i = 0.4502 + 0.00000809IN V STij + 2.1541ST DP ROFij + 0.9166Dji
(0.2631) (0.00000518) (1.8175) (0.3901)
−0.8739(Dji ·ST DP ROFij) + νij
(2.5755) R¯2 = 0.4721 (18)
The coefficient of ST DP ROF is positive and 1.8 times its standard error in equation (17), but only 1.3 times its standard error in equation (18), lending some support to the hypothesis that this variable is a proxy for the flow of information to a firm. However, the coefficient of the interaction term (the product of the A-share dummy and ST DP ROF ) is insignificant by conventional standards in both regressions. The coefficient of IN V ST in the estimated results for equation (18) is significantly positive at the 10% level, lending support to the hypothesis that one reason for greater trading volume (and presumably volatility) in A-share markets is attributable to a larger investor pool available to perceive
news arrivals and initiate trades. The fact that the coefficient of the A-share dummy is positive and significant in the regression results for both equation (17) and (18) indicates that there is much yet to be learned about the nature of the events that leads A-share investors to engage in trading on news not perceived by owners of B A-shares. We conjecture that our ignorance lies in the structure and type of information flows perceived by A- and B-share investors as characterized by the aforementioned maintained hypotheses.
4
Conclusion
In the spirit of Anderson’s MMDH, we estimate a dynamic model of stock returns and trading volumes for China’s domestic A and foreign B shares. We find that news arrives more intensively for A-share investors than for B-share investors, and a larger fraction of news is incorporated into trading volume for A shares, so the volatility of returns is higher for A shares. We find evidence that some of the greater return volatility for A-shares is due to substantially larger number of investors and higher probability of trading on a given “news” item. However, the nature and sources of the “excess” news flowing to A-share market remains, to a great extent, a tantalizing mystery.
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Table 1
Estimation Results for Return-Volume System for A and B Shares
(Standard errors in parentheses and p-values in brackets)
Company µ c m0 m1 α β γ χ219 Shanghai Vacuum A 0.000475 0.1921 1.1265 2.8993 0.0561 0.8796 0.1152 13.707 Electronics (0.000954) (0.0775) (0.4049) (0.9237) (0.0192) (0.1883) (0.0547) [0.8030] B 0.000932 0.4334 0.7562 0.6579 0.0270 0.6420 0.1562 23.065 (0.002075) (0.1514) (0.1968) (0.2297) (0.0101) (0.2278) (0.0727) [0.2441] Shanghai Erfangji A 0.000132 0.2446 0.9875 2.1218 0.0370 0.7938 0.1360 14.596 (0.000073) (0.0864) (0.1253) (0.8399) (0.0104) (0.2561) (0.08614) [0.7604] B 0.000124 0.4439 0.8208 0.8504 0.0006 0.5624 0.0523 19.068 (0.000058) (0.1751) (0.2776) (0.3219) (0.0002) (0.2863) (0.0229) [0.4335] Dazhong Taxi A 0.000563 0.1727 1.6115 2.7234 0.0592 0.7419 0.1788 15.713 (0.001855) (0.0545) (0.5159) (1.2096) (0.0136) (0.1727) (0.0643) [0.6922] B 0.000718 0.3173 1.0082 1.6180 0.0170 0.5398 0.3019 20.324 (0.001907) (0.1422) (0.3089) (0.8066) (0.0057) (0.1699) (0.1521) [0.4017] Yongsheng A 0.001308 0.2977 0.8382 1.7669 0.0453 0.7772 0.1899 14.782 Stationery (0.004492) (0.0946) (0.3806) (0.5026) (0.0138) (0.2989) (0.0885) [0.7567] B 0.001335 0.5232 0.6968 0.9297 0.0153 0.6301 0.1596 19.336 (0.008662) (0.1845) (0.2807) (0.3553) (0.0052) (0.2920) (0.0684) [0.4627] China A 0.000468 0.3983 0.5021 0.4043 0.1368 0.4833 0.2104 22.3862 First Pencil (0.000160) (0.1203) (0.1796) (0.0807) (0.1974) (0.1047) (0.0652) [0.2710] B 0.000718 0.4083 0.5110 0.4136 0.1301 0.2733 0.2074 26.119 (0.000356) (0.1769) (0.2050) (0.1836) (0.0652) (0.0934) (0.1015) [0.1249] China Textile A 0.000549 0.3917 0.4990 1.1042 0.0281 0.7728 0.1981 14.602 Machinery (0.000303) (0.1116) (0.1357) (0.3824) (0.0095) (0.2039) (0.0904) [0.7582] B 0.00103 0.5454 0.4396 0.3608 0.0699 0.6113 0.2831 19.806 (0.000495) (0.1708) (0.1548) (0.1996) (0.0104) (0.2633) (0.1240) [0.4482] Shanghai A 0.000781 0.3339 0.5087 1.4116 0.0422 0.6896 0.2210 17.035 Rubber Belt (0.000185) (0.1412) (0.2166) (0.5372) (0.0164) (0.1990) (0.0703) [0.5448] B 0.000955 0.5100 0.6941 0.5909 0.050 0.5884 0.2092 18.821 (0.000433) (0.1262) (0.2195) (0.1137) (0.014) (0.1706) (0.0711) [0.4902] Shanghai A 0.000564 0.2457 1.0512 2.4070 0.0422 0.7964 0.1136 14.982 Chlor Alkali (0.000208) (0.1033) (0.3144) (0.7675) (0.0185) (0.1309) (0.0341) [0.7801] B 0.00880 0.5849 0.7068 0.6775 0.0779 0.3951 0.2517 24.988 (0.00301) (0.1906) (0.2612) (0.2118) (0.0235) (0.1499) (0.0841) [0.2065] Shanghai Tire A 0.000469 0.2385 0.9181 2.1420 0.0737 0.6158 0.0865 20.268 & Rubber (0.000192) (0.0687) (0.2407) (0.8468) (0.0162) (0.1891) (0.0206) [0.3899] B 0.000703 0.3466 1.1745 1.0869 0.0980 0.3717 0.1206 24.841 (0.000242) (0.1104) (0.3563) (0.2917) (0.0204) (0.1608) (0.0533) [0.1924] Shanghai A -0.000320 0.3982 0.8102 1.4169 0.0384 0.5835 0.2166 18.705 Refrigerator (0.000388) (0.1174) (0.3705) (0.6629) (0.0088) (0.2083) (0.0774) [0.5185] B 0.000144 0.6006 0.5008 0.7908 0.0825 0.4771 0.1002 22.850 (0.000175) (0.1989) (0.1627) (0.2995) (0.0073) (0.1299) (0.0444) [0.2439] Jinqiao Export A 0.000273 0.0433 1.4286 10.8032 0.1285 0.3019 0.0812 74.2219 & Import (0.000139) (0.1017) (0.5338) (0.5965) (0.0110) (0.1862) (0.0498) [0.0001] B 0.000759 0.0584 0.7329 14.0671 0.1565 0.1927 0.2134 100.3204 (0.000256) (0.0649) (0.3940) (3.8158) (0.0042) (0.1186) (0.0792) [0.0001] Outer Gaoqiao A 0.000744 0.4091 0.9151 1.4236 0.0490 0.7990 0.1326 14.2 (0.000267) (0.1380) (0.3377) (0.4891) (0.0038) (0,1881) (0.0592) [0.7861] B 0.001106 0.5667 0.7019 0.4880 0.0150 0.5702 0.1256 18.464 (0.000152) (0.1858) (0.2061) (0.1332) (0.0044) (0.1719) (0.0409) [0.4993] (Continued on next page)
Table 1
(Continued)
Estimation Results for Return-Volume System for A and B Shares
(Standard errors in parentheses and p-values in brackets)
Company µ c m0 m1 α β γ χ219 Shenzhen A 0.000206 0.2989 1.0636 1.5104 0.0050 0.6228 0.1029 19.201 Vanke Co. (0.000202) (0.1046) (0.3619) (0.5727) (0.0008) (0.1941) (0.0523) [0.4286] B 0.000423 0.4913 0.8825 0.6094 0.0117 0.4492 0.1360 23.089 (0.000209) (0.1481) (0.2116) (0.2307) (0.0038) (0.1093) (0.0404) [0.2655] Property & A 0.000851 0.3081 1.0583 1.6192 0.0141 0.7034 0.1799 16.104 Resource Devel. (0.000391) (0.1139) (0.3442) (0.4919) (0.0033) (0.1687) (0.0612) [0.6427] B 0.000397 0.4389 0.9381 1.147 0.0988 0.6725 0.0580 17.552 (0.000196) (0.1117) (0.2036) (0.2250) (0.0241) (0.1973) (0.0084) [0.5208] China A 0.000864 0.3292 0.8417 1.6799 0.0511 0.8220 0.1539 13.928 Southern Glass (0.000435) (0.1409) (0.2762) (0.4990) (0.0098) (0.1905) (0.0482) [0.7886] B 0.000839 0.3825 1.2219 0.8046 0.0481 0.4337 0.2112 23.169 (0.000431) (0.1274) (0.3770) (0.2855) (0.0087) (0.1169) (0.0812) [0.2338] Shenzhen A 0.000435 0.3085 0.2109 0.5684 0.0633 0.2940 0.1806 42.9838 Petroch. Co. (0.000197) (0.1997) (0.1561) (0.2874) (0.0083) (0.1035) (0.6169) [0.0001] B 0.000296 0.1003 0.7107 0.4912 0.1052 0.3616 0.1672 49.4439 (0.000181) (0.1344) (0.4228) (0.2260) (0.0091) (0.1159) (0.1036) [0.0001] Shenzhen A 0.000495 0.3662 0.4819 1.2450 0.0316 0.7636 0.1380 15.066 Zhonghao Co. (0.000217) (0.1261) (0.1475) (0.3927) (0.0089) (0.1903) (0.0424) [0.7403] B 0.000971 0.4838 0.7963 0.5130 0.0605 0.5482 0.1382 20.755 (0.000308) (0.1078) (0.2145) (0.1609) (0.0104) (0.1745) (0.0577) [0.4316] Konka A 0.001029 0.3110 1.2136 1.3301 0.0733 0.5074 0.1337 20.940 Electronics (0.000368) (0.1017) (0.5338) (0.5965) (0.0110) (0.1862) (0.0498) [0.4082] B 0.000725 0.5443 1.0755 0.6081 0.0020 0.5837 0.1993 18.711 (0.000260) (0.2064) (0.4438) (0.2856) (0.0007) (0.2145) (0.0836) [0.5136] Shenzhen A 0.000846 0.3854 0.6512 1.2067 0.0903 0.8074 0.1065 14.225 China Bicycles (0.000315) (0.1275) (0.2369) (0.3675) (0.0258) (0.1363) (0.0319) [0.7714] B 0.001041 0.8147 0.5310 0.3875 0.0889 0.4063 0.2721 24.311 (0.00455) (0.1634) (0.2511) (0.1585) (0.0462) (0.1807) (0.0794) [0.2265] Victor A 0.000580 0.2406 0.8119 2.0240 0.0811 0.6094 0.0750 19.862 Onward Textile (0.000275) (0.0867) (0.2074) (0.6848) (0.0135) (0.1798) (0.0196) [0.4009] B 0.000611 0.3389 1.1477 1.0946 0.0750 0.3622 0.1019 25.401 (0.000298) (0.1047) (0.3365) (0.2829) (0.0154) (0.1806) (0.0421) [0.1885] Shenbao A 0.000309 0.1386 0.5961 0.8119 0.1026 0.2750 0.1143 53.6720 Industry (0.000179) (0.1074) (0.3251) (0.4779) (0.0283) (0.1338) (0.0614) [0.0001] B 0.000157 0.0524 0.6989 5.6237 0.0281 0.3176 0.1608 69.3371 (0.000163) (0.0973) (0.3428) (1.4662) (0.0074) (0.1673) (0.0645) [0.0001] Chiwan Wharf A 0.000296 0.2419 1.134 1.996 0.0805 0.7768 0.1364 14.557 Holdings (0.000125) (0.0715) (0.3228) (0.4197) (0.0120) (0.1655) (0.0351) [0.7288] B 0.000470 0.4386 1.2669 0.4931 0.1022 0.380 0.1904 24.685 (0.000213) (0.1104) (0.3174) (0.1505) (0.0229) (0.1063) (0.0738) [0.2204] China Merchants A -0.000381 0.1098 2.6224 3.8028 0.0437 0.8615 0.0633 13.622 Shekou Co. (0.000227) (0.0414) (0.7231) (0.8655) (0.0096) (0.1417) (0.0244) [0.8125] B 0.000352 0.2773 1.4054 1.1127 0.0699 0.4128 0.1350 24.018 (0.000164) (0.110) (0.3125) (0.2682) (0.0146) (0.1054) (0.0387) [0.2374] Tellus A 0.000199 0.3004 0.8152 1.4663 0.0240 0.7629 0.0835 14.986 Machinery (0.000103) (0.0772) (0.2285) (0.2979) (0.0060) (0.1614) (0.0217) [0.7015] B 0.000983 0.3608 1.0416 0.7239 0.1020 0.4038 0.1295 24.324 (0.000315) (0.1174) (0.2616) (0.2035) (0.0225) (0.1968) (0.0342) [0.2285]
Table 2
Estimates for cm0 and cm1 and Some Distributional Characteristics for the Mixing
Variable
Company cm0 cm1 E(Kt) V ar(Kt) Kurtosis
Shanghai Vacuum A 0.2164 0.557 3.0286 32.0876 455.2750 Electronics B 0.3277 0.2851 1.9784 7.4158 16.3885 Shanghai Erfangji A 0.2415 0.519 2.9869 29.9097 604.8968 B 0.3644 0.3775 1.1685 1.1685 48.9391 Dazhong Taxi A 0.2783 0.4703 3.5048 48.0010 915.0005 B 0.3199 0.5134 2.5243 28.6541 136.4124 Yongsheng A 0.2495 0.526 3.9190 29.2303 795.4628 Stationery B 0.3646 0.4864 1.8443 6.4042 161.9072 China A 0.2 0.161 2.9404 17.2789 181.9652 First Pencil B 0.2086 0.1689 2.2397 7.2794 102.9925 China Textile A 0.1955 0.4325 3.0384 27.2149 353.5309 Machinery B 0.2398 0.1968 2.4247 6.8356 79.0401 Shanghai A 0.1699 0.4713 3.0486 19.8525 127.9680 Rubber Belt B 0.4169 0.3549 2.4179 5.1797 32.9673 Shanghai A 0.3226 0.5642 2.3192 24.6291 358.129 Refrigerator B 0.3008 0.475 1.7771 2.1483 48.6289 Shanghai A 0.2583 0.5914 2.2416 38.2823 100.3267 Chlor Alkali B 0.4134 0.3963 1.9065 7.5179 46.2556 Outer Gaoqiao A 0.3744 0.5824 3.3905 38.3418 396.878 B 0.3978 0.2765 1.1365 2.5558 71.2696 Shenzhen A 0.3179 0.4515 2.4670 3.9808 61.4547 Vanke Co. B 0.4336 0.2994 2.4372 2.1024 22.5456 Property & A 0.3261 0.4989 2.2595 15.8543 216.9141 Resource Devel. B 0.4117 0.5034 2.2417 2.6924 35.6494 China A 0.2771 0.553 4.5870 19.3756 744.2686 Southern Glass B 0.4674 0.3078 1.9940 7.2787 153.5039 Shanghai Tire A 0.1699 0.4713 4.0638 4.8339 75.3546 & Rubber B 0.354 0.3014 1.9229 3.8033 29.1589 Konka A 0.3774 0.4137 4.7095 8.9309 156.1073 Electronics B 0.5854 0.331 2.5890 2.0293 36.2989 Shenzhen A 0.251 0.4651 2.9304 13.2296 268.1887 China Bicycles B 0.4326 0.3157 1.8482 7.9808 146.5652 Victor A 0.1953 0.487 1.9230 2.2616 46.8391 Onward Textile B 0.389 0.371 1.5996 1.5317 16.5769 Shenzhen A 0.1765 0.4559 2.2607 2.5196 66.9716 Zhonghao Co. B 0.3852 0.2482 2.0701 1.8481 27.4972 Chiwan Wharf A 0.2743 0.4828 4.0927 29.5482 439.4244 Holdings B 0.5557 0.2163 2.170 6.7597 101.2753 China Merchants A 0.2879 0.4175 3.0713 15.7529 129.9115 Shekou Co. B 0.3897 0.3086 1.7569 2.8314 29.0362 Tellus A 0.2449 0.4405 1.9187 4.0782 80.7247 Machinery B 0.3758 0.2612 1.8257 3.1546 45.8312
