its trading volume on the Korea Exchange (KRX) from 4

January 2000 to 30 December 2010. Daily index returns

and trading volume were calculated in terms of percent-

age logarithmic change, based on the following formulae:

1

ln 100

ttt

rPP

(1)

1

ln 100

ttt

VTT

(2)

where Pt is the daily close of the index and Tt is the trad-

ing volume.

Figure 1 shows the change in value of the KOSPI and

its trading volume. Prices gradually increased until 2008,

then dropped due to the 2008 global financial crisis, and

then recovered. High trading volume was observed in

2002-2003 and then remained constant.

Table 1 lists the descriptive statistic for KOSPI returns

and its trading volume. Mean return and trading volume

were positive for the market. The kurtosis was positive

for daily stock returns and trading volume, and greater

than 3. Returns skewness was negative and trading vol-

ume skewness was positive. Applying the Jarque-Bera

(J-B) test for normality rejected the null hypothesis of

normality for returns and trading volume. The Q-statistic

can be used to test whether a group of autocorrelations is

significantly different from zero. The autocorrelation coef-

ficient shows that returns did not exhibit a serial correla-

tion whereas trading volume did.

Additionally, we tested the stationarity of returns and

trading volume, for which the most common test is the

2,400,000,000 2,800

0

400,000,000

800,000,000

1,200,000,000

1,600,000,000

2,000,000,000

400

800

1,200

1,600

2,000

2,400

00 0102 03040506 07 080910

TRADE KOSPI

Figure 1. KOSPI index and trading volume.

Copyright © 2012 SciRes. ME

K.-H. CHOI ET AL.

586

unit test. To test for a unit root, we employed both the

augmented Dickey-Fuller (ADF) test and the Phillips-

Perron (PP) test. Table 2 provides the results. The null

hypothesis that returns and trading volume are nonstation-

ary was rejected at the 1% significance level, indicating

that both trading volume and returns are stationary.

4. Methodology

In general, the ARCH model of Engle [15] and the GARCH

model of Bollerslev [16] are the most popular tools for

capturing the volatility dynamics of financial time series.

The GARCH model is particularly useful because it makes

current conditional variance dependent on lags in its prev-

ious conditional variance. One of its primary limitations

is that it enforces a symmetric response of volatility to

both positive and negative market shocks, because cond-

itional variance is regarded as a function of the magnitude

of lagged residuals, not whether they are positive or nega-

tive. However, it has been argued that a negative market

shock may lead to more volatility than a positive shock

of the same magnitude. To account for this, Nelson [1]

developed the EGARCH model and Glosten, Jagannathan

and Runkle [17] introduced the GJR-GARCH model. This

study used both of these models to assess asymmetric

volatility and the effect of new information arrival to the

market.

Table 1. Summary of descriptive statistics.

Returns Trading Volume

Mean 0.0234 0.0163

Median 0.1266 –1.2264

Maximum 11.2843 143.8069

Minimum –12.8047 –92.5004

Std. Dev. 1.8028 18.777

Skewness –0.5513 0.4688

Kurtosis 7.8372 6.0971

J-B 2789*** 1186***

Q(12) 16.526

(0.168)

338.36***

(0.000)

Note: Jarque-Bera (J-B) is the test statistic for the null hypothesis of nomal-

ity in sample returns distributions. Ljung-Box Q(12) statistics test serial

correlations up to a 12th lag length. Significance levels: ***1%, **5%, *10%.

Table 2. Unit root tests for returns and trading volume.

Returns

Trading

Volume

Intercept –51.06*** –25.12***

ADF Test

Trend and Intercept –51.08*** –25.12***

Intercept –51.12*** –180.98***

PP Test

Trend and Intercept –51.15*** –183.08***

Note: The critical value for the ADF and PP tests are –3.9611 and –3.4323

at the 1% significance level, respectively. Significance levels: ***1%, **5%,

*10%; ADF, augmented Dickey-Fuller test; PP, Phillips-Perron test.

The GJR-GARCH (1,1) and EGARCH (1,1) models with

trading volume are defined as follows, respectively:

tt

r (3)

tt

hz

~. ..with0,var1

ttt

ziid Ezz

22

1111tttttt

hhdV

t

(4)

(5)

(6)

11

1

11

2

log log

π

tt

ttt

tt

hhV

hh

2

(7)

where rt is the realized return of KOSPI, μ denotes the

mean of the returns, and Vt is trading volume, which is

used as a proxy for information arrival to the market.

Equation (6) specifies conditional variance as a function

of mean volatility ω, where 1t

is the lag in the squared

residual of the mean (the ARCH term) and provides info-

rmation about volatility clustering, ht – 1 is the previously

forecasted variance (the GARCH term), 11tt

2

d

is a term

that captures asymmetry, and dt – 1 is a dummy variable

that is equal to one if εt – 1 < 0 (bad news) and is equal to

zero if εt – 1 ≥ 0 (good news). When εt – 1 < 0 and dt – 1 = 1,

the effect of an εt – 1 shock on ht is 1t

2

2

1t

. If δ > 0,

negative shocks will have a larger effect on volatility

than positive shocks. In Equation (7), conditional varia-

nce is log-linear, which has several advantages over the

pure GARCH specification. First, regardless of the mag-

nitude of loght, the implied value of ht can never be

negative, but the coefficients can be negative. Second,

instead of using

, EGARCH model uses a standard-

ized value of 11tt

h

, which allows asymmetry to be

considered. Hence, the effect of shock on log conditional

variance is

if 11tt

h

is positive and

if 11tt

h

When trading volume is included in the variance equ-

ation, θ = 0 in both GJR-GARCH (1,1) and EGARCH

(1,1) models when the effect of trading volume on cond-

itional variance is ignored. In the two asymmetric models,

the persistence of conditional variance is measured by

is negative.

, where a larger value indicates greater persis-

tence of market shock. If trading volume is considered a

proxy for information arrival, then it is expected that θ > 0.

If

is smaller when trading volume is included

than when it is excluded, then α or β may be insignificant.

We also tested the relationship between return volatility

and lagged trading volume as follows:

22

11111tttttt

hhdV

(8)

11

11

11

2

log log

π

tt

ttt

tt

hhV

hh

(9)

where Vt – 1 is lagged trading volume. All parameters of

variance in Equations (6)-(9) can be estimated using the

Copyright © 2012 SciRes. ME

K.-H. CHOI ET AL. 587

Brendt, Hall, Hall, and Hausman (BHHH) algorithm,

assuming Student’s t-distribution innovation.

The distribution of the actual returns is shown as the

histogram in Figure 2. The histogram of returns has a more

pronounced peak than a normal distribution, that is, it is

more similar to a t-distribution and, thus, the t-distribution

may be more appropriate to the error term assumption.

Assuming the innovations follow Student’s t-distribution,

the log-likelihood function is defined as follows:

2

π2

2

2

t

1

11

log logloglog

22

1log1log 1

2

T

t

tt

LT

hh

(10)

where the degree of freedom υ > 2 controls the tail be-

havior. The t-distribution approaches normal distribution

as

.

5. Empirical Results

Table 3 shows the estimation results of GJR-GARCH

and EGARCH model excluding trading volume variable.

The coefficients α and β represent ARCH and GARCH

terms, respectively, and are shown to be statistically sig-

nificant at the 1% level. The dynamics of returns exhibit

high persistence in conditional variance. Note that the

asymmetry term, δ, has the correct sign and is significant

at the 1% level. These results imply that good news has a

smaller effect on conditional volatility than bad news,

that is, the market exhibits asymmetry.

Table 4 presents the results when contemporaneous

trading volume is included. The GARCH term

is

statistically significant at the 1% level in both models,

whereas the ARCH term

is significant in EGARCH

Note: Comparison of actual returns distribution to a standardized normal and

Student’s t-distribution. The t-distribution assumes a greater likelihood of

large returns than does the normal distribution.

Figure 2. Returns of the KOSPI.

but not in GJR-GARCH models. The coefficient of trad-

ing volume

is positive and statistically significant at

the 1% level in both models. These results suggest that

contemporaneous volume significantly explains volatility,

supporting the MDH. Including trading volume slightly

increases δ, implying that volume leads to more asym-

metric volatility on the market.

Table 5 shows the estimation results of the two mod-

els when lagged trading volume is included in the condi-

tional variance equation. The estimated coefficients of α,

β, and δ are highly significant but the lagged trading vol-

ume coefficients are not significant. So we conclude that

lagged trading volume does not significantly reduce per-

sistence and does not explain volatility and, thus, does

not support the SIAH.

We evaluated the accuracy of each model specification

using Ljung-Box

12Qs and ARCH (5) tests, as shown

in Tables 4 and 5. Neither test was significant at the 1%

level, indicating that both models are sufficient for meas-

Table 3. Estimation results of GJR-GARCH and EGARCH

models without trading volume.

GJR-GARCH (1,1) EGARCH (1,1)

0.036***

(0.008)

–0.107***

(0.014)

0.021*

(0.012)

0.159***

(0.020)

0.911***

(0.001)

0.979***

(0.004)

0.103***

(0.017)

–0.089***

(0.013)

(12)

s

Q 9.878

[0.541]

14.176**

[0.290]

ARCH(5) 1.041

[0.318]

1.501**

[0.186]

Note: Standard errors are in parentheses and p-values are in brackets. The

Ljung-Box statistic tests serial correlations up to a 12th lag length

in the squared standardized returns. The ARCH(5) statistic tests the ARCH

effects at 5th order lagged, squared residuals. Significance levels: ***1%,

**5%, *10%.

(12)

s

Q

Table 4. Estimation results of GJR-GARCH and EGARCH

models with contemporaneous trading volume.

GJR-GARCH (1,1) EGARCH (1,1)

0.037***

(0.009)

–0.099***

(0.014)

0.0183

(0.007)

0.148***

(0.019)

0.909***

(0.011)

0.977***

(0.004)

0.111***

(0.017)

–0.103***

(0.013)

0.010***

(0.003)

0.007***

(0.002)

12

s

Q 7.675

[0.810]

6.954

[0.861]

ARCH (5) 0.724

[0.605]

0.693

[0.629]

Note: See Table 3.

Copyright © 2012 SciRes. ME

K.-H. CHOI ET AL.

588

Table 5. Estimation results of GJR-GARCH and EGARCH

models with lagged trading volume.

GJR-GARCH (1,1) EGARCH (1,1)

0.037***

(0.008)

–0.107***

(0.014)

0.023***

(0.011)

0.158***

(0.019)

0.912***

(0.011)

0.980***

(0.004)

0.097***

(0.017)

–0.087***

(0.013)

–0.005

(0.003)

–0.001

(0.002)

12

s

Q 10.255

(0.594)

14.190***

[0.289]

ARCH (5) 1.032

(0.397)

1.529

[0.177]

Note: See Table 3.

uring the effects of information arrival to the market, when

trading volume is included.

6. Conclusions

We examined the persistence of return volatility on the

Korean Stock Market (KSM), both including and excluding

trading volume as a proxy for information flow, and con-

sidering lagged volume.

The main conclusions of this study are as follows. First,

the KSM index exhibits strong volatility persistence and

asymmetry. Second, the inclusion of contemporaneous trad-

ing volume in the GJR-GARCH and EGARCH models

results in a positive relationship between trading volume

and volatility. Third, when contemporaneous and lagged

trading volumes are included in the conditional variance

equation, the former is positively correlated with volatil-

ity but the latter is not. Thus, trading volume affects the

flow of information, supporting the validity of MDH.

Finally, the asymmetric effect of bad news on volatility is

higher when contemporaneous trading volume is included,

although market shocks, whether positive or negative, have

similar effects on conditional volatility. Thus, we conclude

that trading volume is a useful tool for predicting the

volatility dynamics of the KSM.

7. Acknowledgements

This work was supported by the National Research Foun-

dation of Korea Grant, funded by the Korean Govern-

ment (NRF-2011-330-B00044).

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