Return and Volatility Spillovers in the Sector

Indexes of the Shanghai Stock Exchange

by

Ali M. Kutan* and Kun Li

Department of Economics and FinanceSouthern Illinois University, Edwardsville

Edwardsville, IL 62026-1102

Abstract

This paper investigates the return and volatility linkages among the five sectors of the Shanghai stock market. Using daily data from August 2, 1999 to March 31, 2001 and employing a battery of symmetric and asymmetric GARCH models, we find unidirectional spillover effects from commerce and industrial sectors to the rest. Despite a uniform pattern for the return linkages, the volatility spillovers tend to exhibit a great deal of interaction. The findings are robust to accounting for the day of the week effects and asymmetric shocks to the volatility. The results have implications for modeling sector returns in Chinese markets as well as for investors and policymakers. These issues are evaluated in the light of empirical evidence and policy implications are discussed.

______________________________________________________________________ *Corresponding author. Email: akutan@siue.edu, Phone: (618) 650-3473, Fax: (618) 650-3047

I. Introduction

The stock market in China has a relatively short history. The Shanghai Stock Exchange

(SHSE) began its operation in December 1990 followed by the Shenzhen Stock Exchange

(SZSE) in July 1991. By January 2001, there were 584 firms listed in SHSE and 514 firms in

SZSE, and the combined capitalization of the markets reached $500 billion, which accounted

for 50% of China’s GDP in 2000. The total investors in the two markets now exceed 50

million.

Despite the short history of the market and difficulty in obtaining data, research on

Chinese financial markets has been growing. There is now an influential body of literature

analyzing the Chinese stock market from various angles. For example, Mookerjee and Yu

(1999) tested the market efficiency and uncovered significant inefficiencies present in both

SHSE and SZSE. Xu (2000) provided a general review of the microstructure of the Chinese

stock market. Song and Liu (1998) examined the price and volatility spillover effects between

SHSE and SZSE while Chui and Kwok (1998) studied the linkages between A and B shares.

Poon et al. (2000) investigated the link between China-backed shares in the overseas markets

and those in the domestic market. Huang et al. (2000) examined the causality and

cointegration relationship among the stock markets of China, Japan, and the U.S.

The issue of return and volatility is extensively studied in the literature [see Booth et al.

(1997) and Huang et al. (2000) for a review of recent studies], but the major focus has been on

either the linkages between stock markets of different countries or different types of financial

markets within a given country. A few of the existing research have addressed the issue of

return and volatility linkages between sectors within a given stock market, however. Studying

the pattern of returns and volatility between sectors and how they may interact with each other

1

is important for the efficient asset allocation decisions and empirical modeling of sector

returns. This paper proposes to fill this gap in the literature by examining the return and

volatility linkages at the sector level in SHSE.1 In doing so, we are also able to extend the

earlier studies on the Chinese stock market and moved the attention to a more micro-level. Our

findings have significant implications for investors regarding portfolio diversification, central

banks concerning the “contagion” of volatility between sectors, and practitioners who are

interested in empirical modeling of stock markets at a micro level.

The rest of the paper is organized as follows. In Section II, we outline the methodology

used in this study. In Section III we describe our data and present the empirical results. Section

IV discusses the implications of the results for policymakers and investors, and concludes the

paper.

II. Methodological Issues

Evidence indicates that Chinese stock returns are autocorrelated and their conditional

variance exhibits ARCH effects [Hu et al. (1997) and Su and Fleisher, (1998)]. It is reasonable

to assume that the same characteristics would hold for sector-level data. We therefore employ a

generalized autoregressive conditional heteroskedasticity (GARCH) model to study the return

and volatility linkages between the five Chinese sector indexes.

The GARCH models consist of a mean equation, as well as, a conditional variance

equation. The mean equation employed in this study includes an autoregressive component to

account for serial autocorrelation in returns. To test for spillover effects among sector returns,

data on lagged returns of other sectors are included in the mean equation. Similarly, we

include the data in the conditional variance equation to test for volatility spillover effects.

1 We choose SHSE instead of SZSE, because data on sector indexes in SHSE is more complete.

2

China continues to liberalize its financial markets and we expect an increase in the

influence of international equity markets on the Chinese market. Earlier studies do not study

the impact of global market changes on stock market “volatility” in China, but they study the

link between returns (Huang et al., 2000). To account for this effect, we also include U.S.

index (S&P500) returns in the variance equation as a proxy to represent global market

developments. A statistically significant coefficient for the world index in the mean (variance)

equation would indicate significant return (volatility) spillovers from global equity markets to

the Chinese stock market.

Previous studies show that a simple GARCH(1,1) specification is a good fit for

modeling stock market returns in China [Hun et al. (1997) and Yeh and Lee (2000)]. Thus, the

mean equation employed in this paper can be specified as:

(1)

where Rst is the return for index s at time t, where s=1,…6 (1=Industry, 2=Commerce,

3=Conglom, 4=Utility, 5=Property, 6=S&P500). The sector returns are expressed in terms of

their lagged values to avoid the simultaneity bias in estimations. The U.S. index is adjusted for

the difference in time zones between the two markets. The daily returns are calculated as the

log-differenced closing price index, multiplied by 100. m is the number of lags of the

independent variables, which we determine based on the Akaike and Schwarz information

criteria. The conditional variance equation of the GARCH(1,1) model can be written as:

(2)

where ε2t-1 refers to the last period's surprise in average returns and is the last period's

conditional variance.

3

The day-of-the-week effects exist in many stock markets.2 To test the significance of

the day-of-the-week effects in both sector return and volatility, we include a set of dummy

variables Djt in both the mean and the variance equations. Djt represents (0,1) dummy variables

for Monday through Friday. The mean and variance equations with the day-of-the-week effects

can be written as:

(3)

(4)

In the variance equation, we drop the dummy variable for Wednesday to avoid co-linearity in

the estimations.

It is possible that equity markets react differently to good and bad news. Upward

movements due to good news may have lower volatility than downward movements of the

same magnitude due to bad news. To test the existence of the asymmetric news for sector

returns in SHSE, we also employ an EGARCH (1,1) model. The mean equation in the

EGARCH model is same as equation (3), but its conditional variance is modified as a function

of lagged returns of other sectors, the natural logarithm of past conditional variances, and past

volatility shock. This model can be written as:

(5)

Note that the left-hand side of the variance equation is in log form, so the asymmetric effect

captured by the EGARCH model is exponential. The presence of such effects can be tested by

2 Cheung and Ng (1992) find day-of-the-week effects for U.S. stock returns and Poon and Fung (2000) and Xu (2000) report day-of-the-week effects in SHSE volatility.

4

the alternative hypothesis that the estimated coefficient for is significantly different from

zero.

III. Empirical Results

Data

We use daily closing price of the S&P500 and five sector indexes as listed on the

SHSE. The sector data are taken from the SHSE web site, www.sse.com.cm/. Our sample

period starts from August 2, 1999 and ends in March 31, 2001, containing 18 months of data.3,4

Figure 1 provides a plot the five sector indexes as classified by the SHSE, which are: industry,

commerce, property, public utility, and conglomerate.

Table 1 gives a summary of the sector structure of SHSE as of January 2001. Industry,

Conglomerate, and Commerce are the largest sectors with the industry sector dominating the

market with about 60% of the market share.

Descriptive Statistics

Table 2 provides some descriptive statistics for the returns. They are all positive except

that of S&P500. The standard deviation of the sector returns is much higher than that of

S&P500, indicating that higher risk is associated with higher returns. All the returns are

positively skewed and the excess kurtosis and skewness measures indicate non-normal

distribution. The Jarque-Bera tests confirm this by rejecting the null hypothesis that the sector

returns are normally distributed. This is consistent with the evidence reported in previous

studies (Long et al., 1999). The reported kurtosis and skewness values for the sector returns

3 Although the SHSE began to publish sector indexes in January 1997, the data are incomplete for the first two years.4 Due to the different holiday patterns between the U.S. and China, for the days during which there is no trading for SP500, we simply use the price of the previous trading day

5

are much higher than that of SP500, indicating much higher returns in the SHSE relative to that

of SP500.5

In the next section, we first report the results for the GARCH (1,1) model without the

day-of-the-week effects and asymmetric terms. Then we relax these assumptions and report

the findings for the day-of-the-week and asymmetric effects to examine the sensitivity of the

findings to different specifications.

Empirical Results

To choose an optimal lag length for our variables in the mean and variance equation, the

GARCH (1,1) models are first estimated with up to 10 lags, using the Bollerslev-Woldridge

robust standard errors. Table 3 reports the Akaike and Schwarz information criteria based on

each lag selection. The results from both tests equivalently indicate that one-lag model is

preferred over the other ones. This finding suggests a speedy reaction of markets to

developments in others.6

Table 4 reports the estimated coefficients for the GARCH(1,1) model, as given by

equations (1) and (2). The results for the mean equation reveal significant spillover effects

from the commerce and industry sectors to others. Movements in the commerce sector shares

are significant and positive in each equation, indicating significant spillover effects from this

sector to the rest. Although the number of firms in the commerce sector makes up less than

10% of the total number of listed firms in SHSE, these firms are often small-sized and they can

successfully influence the market as institutional investors.7 Industry returns also have

significant but negative spillover effects on other sectors, except commerce. This negative

5 To account for the non-normality of the returns, all estimations in the following sections are conducted using the Bollerslev-Woldridge robust standard errors.6 This evidence is consistent with other studies. See, for example, Huang et al. (1997) and Kim et al. (2000).7 The manipulation of the market by the speculative institutional investors is a prominent problem in Chinese stock markets.

6

relationship between the industry and other sector returns in the mean equation indicates

portfolio diversification gains. The large size of the market may explain the significance of the

industry sector (Table 1).

The coefficients for conglomerate, property, and utility returns in the mean equation are

not statistically significant, indicating no spillover effects running from these sectors to others.

The estimated coefficient for the S&P500 return is not significant in the mean equation for all

sectors either, suggesting no information flows transmitting from the U.S. market to the

Chinese market. The largely closed financial sector of China appears to be still shielding the

market from any wealth effects arising from global stock market developments. This evidence

is consistent with earlier studies (Huang et al. 1997).

Turning to the results for the conditional variance equation, we observe that the ARCH and

the GARCH coefficients are positive and the sum of the two is less than unity in all models,

except for property where the coefficient for the ARCH term is significant but negative.8

Contrary to an uniformed pattern of spillover effects from the commerce and industry sectors

to others in the mean equation, the results for the conditional variance equation indicate a great

deal of interaction of volatility between the sectors. This finding suggests that there is

significant transmission of volatility across sectors.

The coefficient for the S&P500 returns is significant in the volatility equation for

industry, utility, and conglomerate sectors. The estimated coefficient is negative, suggesting

that an increase in the U.S. market returns tends to reduce the conditional variance of these

sector returns in China.9 This result indicates that investors in China can reduce portfolio risk

by holding sector assets along with the S&P500 index. One potential explanation of this

8 This negative sign disappears when an asymmetric model is employed in the next section. 9 As mentioned earlier, Huang et al. (1997) does not study the impact of international markets on volatility on Chinese stock markets. Our evidence indicates volatility linkages between the U.S. and Chinese markets.

7

finding is that U.S. stock market developments may act as a proxy for information arrival

(Huang et al. 1997), affecting directly the conditional volatility of sector indexes in China.

Table 4 also reports some diagnostic tests. The Q test statistics for the estimated

residuals and Q2 statistics for the squared residuals show that no serial correlation and ARCH

effects, respectively, indicating that a simple GARCH(1,1) model generally fits the patterns of

returns and volatility of the sector indexes in China well, which is consistent with earlier

studies’ findings.

Weekday Effects

Table 5 reports the results of estimating Equations (3) and (4) jointly, which includes the

day-of-the-week effects. None of the coefficients for the day-of-the-week effects in the mean

equation is statistically significant at the 5% level, indicating no significant day-of-the-week

effects present at the sector level data in China. 10As expected, adding the effects in the mean

equation does not affect the results reported in Table 4. The spillover effects of returns from

the commerce and industry sectors are still significant in Table 5.

Many of the coefficients for the day-of-the-week effects in the conditional variance

equation are significant and negative, however. The negative sign indicates that market

volatility relative that that of Wednesday is lower. Again, there is no one fixed-pattern of

volatility linkages observed between the sectors. An interesting finding is that the inclusion of

the day-of-the-week effects increases the significance of volatility spillover effects. In

addition, the estimates for property returns now provide a better fit for the data, as the

estimated Q statistics of the squared residuals for this sector is no longer statistically

significant.

Asymmetric Effects

10 Xu (2000) also finds no significant day-of-the week effects for the composite index returns in China. 8

Table 6 reports the results for the asymmetric effects by providing estimates of Equation

(5) as well. The results show that the commerce and property sectors have significant

asymmetric effects, as the estimated γ coefficient is statistically significant at the 10% level or

better. The asymmetric term has a positive sign, indicating that higher volatility is associated

with good news than with bad news. The reported results do not affect the significance level of

other independent variables, however. The commerce and industry sectors are still significant

in each equation. Overall, our results appear to be quite robust to using an asymmetric

specification for the conditional variance equation as well.

IV. Policy Implications and Conclusions

We have examined the return and volatility linkages between the five sector indexes of

SHSE. To our knowledge, this is the initial study in the literature. We have found that the

commerce and industry sectors are the most influential ones. In particular, the finding that the

industry sector exhibits negative spillover effects with the returns of other sectors is useful for

portfolio construction, suggesting that investors can reduce their portfolio risk by combining

assets from this and other sectors. In addition, there is a great deal of volatility linkages across

the sectors. These results also have implications policymakers. Our findings suggest that can be

easily transmitted between sectors to others. Policymakers may design appropriate

macroeconomic policies to reduce the potential undesirable effects of “volatility contagion”

between sectors.

Our analysis has showed no significant wealth effects in SHSE arising from the U.S. stock

market developments. However, movements in the U.S. stock market are found significant in

9

the conditional variance equation for some sectors, suggesting that investors can further reduce

portfolio variance by combining relevant sector shares with the S&P500 index accordingly.

The empirical results have indicated no significant day-of-the-week effects in sector

returns, but in their volatility for some sectors. The asymmetric information effect is also

detected in the commerce and property sectors. These results have important implications for

modeling sector returns in the Chinese market.

Overall, this study has provided some preliminary results on the behavior of the SHSE

at the micro-level, revealing some interesting observations. Due to lack of a longer data set,

we are not able to investigate the issue of long-run linkages between sectors. It is important to

note that the industry classifications used in this paper is also far from accurate. The regulators

of the Chinese stock market have recently adopted a new criterion for industrial classification.

This regulatory change can help better capture the sector linkages and the results may be

sensitive to this new classification. As a result, we believe that further studies on the sector

behavior in the Chinese stock markets will be rewarding. We hope that the initial findings from

this study will provide some benchmark results for future studies.

10

REFERENCES

Booth, G.B, Martikainen, T., Tse, Y. (1997). “Price and Volatility Spillovers in Scandinavian

Stock Markets”, Journal of Banking and Finance, 21, 811-823

Chui, A.C.W, Kwok, C.C.Y. (1998). “Cross-autocorrelation between A Shares and B Shared in

the Chinese Stock Market”, Journal of Financial Research, 21(3), 333-353.

Huang, B, Chin-Wei, Y and Hu, J.W. (2000) “Causality and Cointegration of Stock Markets

among the United States, Japan, and the South China Growth Triangle”, International

Review of Financial Analysis, 9(3), 281-297.

Kim, M., Szakmary, A. and Mathur, I. (2000). “Price Transmission Dynamics Between ADRs

and Their Underlying Foreign Securities”, Journal of Banking and Finance 24 (8),1359-1382.

Long, D. M., Payne, J. D. and Feng, C. (1999). “Information Transmission in the Shanghai

Equity Market”, Journal of Financial Research, 22, 29-45

Mookerjee, R. and Yu, Q. (1999). “An Empirical Analysis of the Equity Markets in China”

Review of Financial Economics 8, 41-60.

Poon, W. P.H. and Fung, H. (2000). “Red Chips or H Shares: Which China-Backed Securities

Process Information the Fastest?” Journal of Multinational Financial Management, 10,

315-343.

Song, H. and Liu, X. (1998). “Stock Returns and Volatility: An Empirical Study of Chinese

Stock Markets”, International Review of Applied Economics, 12, 129-140.

Su, D. and Fleisher, M. (1998). “Risk, Return and Regulation in Chinese Stock Markets”,

Journal of Economics and Business, 50, 239-256.

Xu, C.K. (2000). “The Microstructure of the Chinese Stock Market” China Economic Review

11, 79-97.

Yeh, Yin-Hua and Lee, Tsun-Siou (2000). “ The Interaction and Volatility Asymmetry of

Unexpected Returns in the Greater China Stock Markets ” Global Finance Journal, 11,

129-149.

11

Table 1. The Sector Structure of SHSE

Industry Commerce Property Utility Conglom. Total

Number of Firms 354 54 9 53 114 584

Percentage (%) 60.62 9.25 1.54 9.07 19.52 100

Source: SHSE (www.sse.com.cn/)

12

Table 2. Descriptive Statistics of Daily Returns

S&P500 Industry Commerce Property Utility Conglo.

Mean -0.0338 0.0733 0.092 0.0408 0.0715 0.0493

Std. Dev. 0.13918 1.3531 1.5616 1.7977 1.3702 1.3737

Skewness 0.0247 0.6884 0.4203 0.2690 0.4870 0.07484

Kurtosis 4.52 8.63 7.46 6.19 8.09 9.66

Jarque-Bera 37 553 338 171 440 765

Probability 0.00 0.00 0.00 0.00 0.00 0.00

Notes: The daily returns are computed as 100 times the difference in the logarithmic of closing stock prices. The sample period runs from August 2, 1999 to March 31, 2001.

13

Table 3. Lag Selection Tests: Akaike and Schwarz Critieria

Number of lags

Industry Commerce Property Utility Conglom.

1 3.303.46

3.443.59

3.894.04

3.403.55

3.313.46

2 3.343.60

3.453.66

3.944.20

3.413.68

3.383.64

3 3.333.71

3.453.82

4.004.38

3.443.82

3.373.75

4 3.413.90

3.554.04

4.044.53

3.463.94

3.343.83

5 3.434.06

3.614.24

4.064.68

3.524.15

3.394.02

6 3.424.13

3.604.31

4.084.79

3.524.25

3.344.14

7 3.474.30

3.694.52

4.134.96

3.534.36

3.504.33

8 3.484.43

3.794.73

4.245.18

3.594.53

3.524.46

9 3.754.80

3.924.98

4.305.35

3.794.85

3.734.79

10 3.714.88

3.965.14

4.395.57

3.694.86

3.744.91

Note: The first line reports the Akaike and the second Schwarz criteria. All results are based on the standard GARCH (1,1) model. Lags are included in both the mean and variance equations.

14

Table 4. GARCH(1,1) Model Estimates

Variable Industry Commerce Property Utilities Conglom

Mean equation

Constant 0.08 0.04 0.07 0.08 -.0.00

Conglom(-1) 0.06 -0.09 -0.11 -0.01 -0.04

Property(-1) 0.06 0.02 0.06 0.06 -0.04

Commerce(-1) 0.35** 0.33** 0.58* 0.37* 0.33*

Utility(-1) 0.04 0.02 0.19 0.12 0.12

Industry(-1) -0.45** -0.20 -0.77* -0.51* -0.35**

SP500(-1) -0.04 -0.01 0.02 -0.04 -0.05

Variance Equation

Constant 0.06 0.30* 0.01 0.59** 0.43*

ARCH(1) 0.11* 0.29* -0.01 0.11** 0.15*

GARCH(1) 0.85* 0.59* 1.00* 0.57* 0.61*

Conglom(-1) -0.11 0.24 -0.15 0.40 NA

Property(-1) -0.03 -0.17* NA -0.15** -0.14*

Commerce(-1) 0.12 NA 0.33* 0.06 0.32**

Utility(-1) -0.09 -0.18 -0.07 NA -0.41*

Industry(-1) NA -0.01 -0.14 -0.31 0.06

SP500(-1) -0.13* -0.06 -0.00 -0.22* -0.15*

Log-likelihood -635 -662 -751 -654 -636

Q(10) 8.27(0.60)

5.39(0.86)

3.47(0.97)

12.46(0.25)

7.93(0.63)

Q2(10) 5.25(0.87)

9.93(0.44)

24.47*(0.00)*

4.44(0.93)

7.26(0.70)

Note: For Q and Q² tests, the values in parentheses refer to p-values. A p-value less than .10 indicates rejection of the null hypothesis that there is no serial correlation and ARCH effects at the 10 percent significance level, respectively. * : significant at the 1% level. ** :significant at the 5% level. *** :significant at the 10% level.

15

Table 5. GARCH (1,1) Estimates with the Day-of-the-Week Effects

Variable Industry Commerce Property Utilities Conglom

Mean Equation

Constant 0.07 0.05 0.08 0.08 -0.01

Conglom(-1) -0.07 -0.04 -0.13 -0.02 0.11

Property(-1) 0.07** 0.07** 0.08 0.07** 0.04

Commerce(-1) 0.27** 0.27** 0.60* 0.34** 0.22**

Utility(-1) 0.08 0.11 0.03 0.12 0.03

Industry(-1) -0.35** -0.37** -0.66* -0.51** -0.37**

SP500(-1) -0.05 0.03 0.01 -0.02 -0.04

Mon -0.02 0.05 0.02 0.14 -0.18***

Tue 0.15 -0.05 0.05 0.11 0.15

Wed -0.01 -0.02 -0.11 0.09 -0.06

Thu -0.11 0.14 0.05 0.11 0.10

Fri 0.05 0.08

0.09 0.04 0.01

Variance Equation

Constant 0.42* 1.15* 1.24* 0.91* 0.49**

ARCH(1) 0.00 0.26* -0.04* 0.15* 0.08*

GARCH(1) 0.98* 0.64*

1.00* 0.60* 0.87*

Conglom(-1) -0.02 0.05 0.49* 0.29 NA

Property(-1) -0.07* -0.08 NA -0.08*** -0.11*

Commerce(-1) 0.10* NA 0.20** -0.05 0.03***

Utility(-1) -0.05* -0.13 0.08 NA -0.03

Industry NA 0.16 -0.89* -0.16 0.00

SP500(-1) -0.02 -0.08*** -0.01 -0.14** -0.11*

Mon -0.55 -0.72** -0.75 0.03 -0.00

Tue -0.65* -1.38* -2.14* -1.17* -0.55**

Thu -0.91* -1.29** -2.15* -0.27 -0.48

Fri -0.01 -1.23* -0.54 -0.93** -0.54

Log-likelihood -609 -654 -737 -652 -623

Q(10) 10.08(0.43)

6.59(0.76)

2.31(0.99)

11.92(0.29)

6.99(0.73)

Q2(10) 4.43(0.92)

6.26(0.79)

9.02(0.53)

4.39(0.93)

5.52(0.85)

Note: See Table 4

16

Table 6. Asymmetric Effects-EGARCH(1,1) Model Estimates

Variable Industry Commerce Property Utilities Conglom

Mean Equation

Constant 0.08 0.03 0.06 0.07 -.0.01

Conglom(-1) -0.01 -0.01 0.03 -0.11 -0.06

Property(-1) 0.05 0.03 0.04 0.09** 0.04

Commerce(-1) 0.40* 0.19 0.30* 0.40* 0.31*

Utility(-1) 0.06 0.11 0.20 0.10 0.05

Industry(-1) -0.50** -0.28 -0.51** -0.49** -0.31***

SP500(-1) -0.03 -0.02 0.00 -0.03 -0.03

Monday 0.05 -0.01 0.02 0.10 -0.18***

Tuesday 0.07

0.04 -0.06 0.09 0.02

Wednesday 0.01 0.07 -0.19 0.07 -0.08

Thursday -0.01 -0.11 0.24 -0.09 -0.06

Friday 0.04 0.06 0.25 0.03 0.06

Variance Equation

Constant 0.31* 0.37* 0.72* 0.27* 0.31*

-0.09*** -0.04 0.33* -0.07 -0.05

-0.13 0.16*** 0.48* -0.04 0.06

EGARCH(1) 0.97* 1.00* 0.40* 0.98* 0.99*

Conglom(-1) 0.14 0.09 -0.27 0.08 N/A

Property(-1) -0.08* -0.06** N/A -0.06** -0.05***

Commerce(-1) -0.01 N/A -0.01 0.01 0.10**

Utility(-1) 0.01 -0.03 -0.29*** N/A -0.01

Industry(-1) N/A -0.12 0.44*** -0.03 -0.15

SP500(-1) 0.01 -0.00 -0.09*** 0.00 -0.02

Monday -0.11 -0.19 -0.06 -0.21 -0.16

Tuesday -0.52** -0.62* -0.78* -0.45 -0.45***

Thursday -0.33 -0.48** -0.56 -0.06 -0.32

Friday -0.29 -0.43*** -0.54** -0.41 -0.43

Log-likelihood -606 -641 -752 -627 -597

Q(10) 8.21(0.61)

7.96(0.66)

2.02(0.99)

13.72(0.19)

8.87(0.54)

Q2(10) 4.18(0.93)

12.65(0.24)

19.22**(0.038)**

3.21(0.98)

5.93(0.82)

Note: See Table 4.

17

18

Figure 2: Daily Returns of Sector Indexes (%)

19

20