Relationship between Trading Volume and Asymmetric Volatility in the Korean Stock Market

doi:10.4236/me.2012.35077

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Modern Economy, 2012, 3, 584-589

http://dx.doi.org/10.4236/me.2012.35077 Published Online September 2012 (http://www.SciRP.org/journal/me)

Relationship between Trading Volume and Asymmetric

Volatility in the Korean Stock Market

Ki-Hong Choi1, Zhu-Hua Jiang2, Sang Hoon Kang3, Seong-Min Yoon1*

1Department of Economics, Pusan National University, Busan, Korea

2Research Institute of Social Criticality, Pusan National University, Busan, Korea

3Department of Business Administration, Pusan National University, Busan, Korea

Email: *[email protected]

Received May 27, 2012; revised June 25, 2012; accepted July 5, 2012

ABSTRACT

We investigated the relationship between return volatility and trading volume as a proxy for the arrival of information

to the market, based on Korean stock market (KSM) data from January 2000 to December 2010. We measured the rela-

tionship between return volatility and trading volume using the GJR-GARCH and exponential GARCH (EGARCH)

models. We found a positive relationship between trading volume and volatility, suggesting that trading volume influ-

ences the flow of information to the market. This finding supports the validity of the mixture of distributions hypothesis.

Considering that trading volume can also explain volatility asymmetry, we conclude that trading volume is a useful tool

for predicting the volatility dynamics of the KSM.

Keywords: Asymmetry; Volatility; Trading Volume; Mixture of Distribution Hypothesis

1. Introduction

Volatility exhibits three typical patterns in most financial

time series, namely, clustering, asymmetry, and persistence.

In particular, many empirical studies have identified asym-

metric volatility, by which stock return volatility tends to

rise more following a large fall in price (bad news) than

following a rise in price (good news) (Nelson [1]; Engle

and Ng [2]). We investigated the effects of trading volume

on asymmetric volatility in the Korean stock market (KSM),

by studying the relationship between volatility and trading

volume as a proxy for the arrival of information (herea-

fter, information arrival) to the market.

We examined the relationship between stock returns

and trading volume using the mixture of distributions

hypothesis (MDH), in the context of information arrival.

The MDH provides an explanation for volatility and

volume by linking changes in price, volume, and the rate

of information flow. The MDH implies a positive relat-

ionship between trading volume and volatility, as price

changes simultaneously. Shifts to new equilibrium are

immediate, and no intermediate processes form.

Many empirical studies supporting the MDH have exp-

lained volatility persistence by including trading volume

as a proxy for information arrival using the general auto-

regressive conditional heteroskedasticity (GARCH) model.

But almost none of these studies considered asymmetric

GARCH models. This study used the daily stock index

and its trading volume on the KSM to explore the rela-

tionship between asymmetric volatility and trading volu-

me, using two asymmetric GARCH models; exponential

GARCH (EGARCH) and Glosten-Jagannathan-Runkle-

GARCH (GJR-GARCH) models.

The remainder of this paper is organized as follows. A

literature review is presented in Section 2. Section 3 pre-

sents the data and descriptive statistics. Section 4 presents

the methodology of the study. The empirical results are

discussed in Section 5. Section 6 concludes the paper.

2. Literature Review

Economists have long been interested in studying the

relationship between stock return volatility and trading

volume. Studies on this relationship are usually theoreti-

cally based on either the sequential information arrival

hypothesis (SIAH) or the MDH.

The seminal study of Copeland [3] assumed that traders

receive new information in sequential random style; acco-

rdingly, he developed the SIAH. The traders change their

trading positions as new information arrives to the market.

However, not all traders receive this new information at

exactly the same time. Hence, the response of each indi-

vidual trader to this information represents an incomplete

equilibrium. The final market equilibrium is established

when all traders have received the information and have

made a trading decision based on that information. Thus,

*Corresponding author.

K.-H. CHOI ET AL. 585

the SIAH suggests that a lead-lag relationship between

volume and volatility exists only in the presence of inf-

ormation.

However, the MDH offers a different explanation by

linking changes in price, volume, and rate of information

flow (Clark [4]; Epps and Epps [5]; Harris [6]). The MDH

implies a positive relationship between trading volume

and price variability, and this relationship is a function of

a mixing variable defined as the rate of information flow.

In the MDH, the shift to a new equilibrium is immediate,

and the partial equilibrium of the sequential information

model never occurs. Clark [4] introduced this concept,

which explores the role of trading volume as a proxy for

a stochastic process of information arrival, for theoretically

analyzing trading volume and the movement of stock

prices.

Lamoureux and Lastrapes [7], testing the relationship

between volume and volatility for a number of actively

traded stocks in the United States, used contemporaneous

trading volume as an explanatory variable in the variance

equation and found that the inclusion of volume eliminated

the persistence of volatility. Gallo and Pacini [8], using

data on 10 actively traded US stocks from 1985 to 1995,

found that persistence decreased when trading volume

was used in the conditional variance equation. Foster [9]

tested the predictions of MDH for the oil futures market

from 1990 to 1994 and found that volume and volatility

were largely contemporaneously related and that both

were driven by the same factor, which is assumed to be

information arrival. Alsubaie and Najand [10] tested the

effect of trading volume on the persistence of the con-

ditional volatility of returns in the Saudi stock market.

Overall, their results supported the MDH at the firm level.

However, not all studies support the MDH. For example,

Sharma, Mbodja and Kamath [11] investigated the relati-

onship between trading volume and volatility for the New

York Stock Exchange (NYSE) index from 1986 to 1989.

They found that trading volume did not completely explain

the GARCH effect, and concluded that while trading

volume might be a good proxy for information arrival

about individual firms, it is not true for the market as a

whole. Lee [12] investigated the relationship between

trading volume and volatility of Korean markets using

the threshold GARCH (TGARCH) model and found that

there was asymmetric volatility in the Korea Composite

Stock Price Index (KOSPI) and the Korean Securities

Dealers Automated Quotations (KOSDAQ) market, but

concluded that inclusion of trading volume did not reduce

volatility persistence in the conditional variance equation.

An, Jang and Lee [13] examined the contemporaneous

correlation as well as the lead-lag relationship between

trading volume and return volatility on the Korean stock

market and found evidence of a significant lead-lag rela-

tionship between trading volume and the return volatility

using the SIAH. Kim and Kim [14] investigated the rela-

tionship between return volatility and volume of the KOSPI

200 futures index using the GJR-GARCH model. They

identified volatility persistence, asymmetric responses to

information arrival, and a relationship between return

volatility and volume.

3. Data and Descriptive Statistics

Our primary data set consisted of a daily stock index and

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:





ln 100

ttt

rPP





(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

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.

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:

r (3)











 

~. ..with0,var1

ttt

ziid Ezz

1111tttttt

hhdV

(4)

(5)

(6)



 



 

log log

ttt

hhV















 





(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





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











. 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





, which allows asymmetry to be

considered. Hence, the effect of shock on log conditional

variance is











if 11tt





 is positive and











 if 11tt





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.











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:

11111tttttt

hhdV

 





 (8)

log log

ttt

hhV



 









 (9)

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

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

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:



 

π2







































log logloglog

1log1log 1









 

 



 

 





















(10)

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

havior. The t-distribution approaches normal distribution



.

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







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)

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)

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)





Q 7.675

[0.810]

6.954

[0.861]

ARCH (5) 0.724

[0.605]

0.693

[0.629]

Note: See Table 3.

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)



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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