Empirical Study on Overreaction and Underreaction in Chinese Stock Market Based on ANAR-TGARCH Model

doi:10.4236/jfrm.2013.24012

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Journal of Financial Risk Management

2013. Vol.2, No.4, 71-76

Published Online December 2013 in SciRes (http://www.scirp.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2013.24012

Open Access 71

Empirical Study on Overreaction and Underreaction in Chinese

Stock Market Based on ANAR-TGARCH Model

Yong Fang1,2,3

1Post-Doctoral Scientific Research Workstation, Shanghai International Group Co., Ltd. (SIG), Shanghai, China

2Post-Doctoral Research Station for Applied Economics, Fudan University, Shanghai, China

3Department of Applied Mathematics, Shanghai Finance University, Shanghai, China

Email: [email protected]

Received July 26th, 2013; August 26th, 2013; September 5th, 2013

tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original

work is properly cited.

An ANAR-TGARCH model is adopted in this paper. By using a first-order asymmetric autoregressive

mean equation, we conduct a series of robust tests on overreaction and underreaction in the Chinese stock

market by taking the abnormal value, run length, time scale, size, industry, style, and market cycle into

account. We then comprehensively compare the intensities of the first-order autocorrelation by using

Wald coefficients tests. Results could provide strong empirical support for generating stock market in-

vestment strategies.

Keywords: Overreaction; Underreaction; ANAR-TGARCH Model

Introduction

Since the mid-1980s, behavioral finance has rapidly risen

and become an entire theory system. Behavioral finance dem-

onstrates broad prospects because of its theoretical analysis of

real investment behavior, and causes significant changes in

modern financial theory structure and financial research para-

digm (Kahneman & Tversky, 1979; Thaler, 1985; De Long,

Shleifer, Summers, & Waldmann, 1990a; De Long, Shleifer,

Summers, & Waldmann, 1990b; Gervais & Odean, 2001; Bac-

chetta & Wincoop, 2008; Barberis, Huang, & Santos, 2001).

Overreaction or underreaction to information is one of the

important behavioral characteristics of investors with limited

rationale. A number of empirical studies reported that stock

returns show significant autocorrelation. Traditional financial

theory based on the rational person hypothesis cannot provide a

reasonable explanation for this phenomenon. Behavioral fi-

nance attributes the significant autocorrelation of stock returns

to the biased reaction of investors to new information, including

overreaction and underreaction. Thus, as new information ap-

pears, investors cannot revise their views according to the

Bayesian rule.

In behavioral finance theory, many classical models are used

to analyze the overreaction or underreaction of investors. Bar-

beris, Shleifer, & Vishny (1998) assumed that investors have

two kinds of mental biases when making investment decisions.

One is the representative bias, in which investors make infer-

ences and judgments according to a small sample and ignore

the population. Another is the conservative bias, in which in-

vestors are unable to update their expectations in a timely

manner according to new information. The representative bias

causes overraeaction and the conservative bias causes underre-

action to new information. Daniel, Hirshleifer, & Subrah-

manyam (1998) explained overreaction and underreaction from

another perspective. They divided all investors into informed

and uninformed investors. Uninformed investors do not have

mental biases but informed investors do. These mental biases

include overconfidence and self-attribution. Commonly over-

confident, informed investors depend excessively on private

information and underestimate the value of public information.

Such investors likewise overestimate their ability to forecast

and underestimate their forecasting error. Overconfidence can

lead to mispricing of stocks. Generally, overconfidence is usu-

ally encouraged by another mental bias, namely, self-attribution,

which is when investors attribute their success to their own

abilities and attribute failure to external noise. De Bondt &

Thaler (1985) sorted all stocks listed in the New York Stock

Exchange according to accumulated returns over the past years

and constructed two portfolios. One portfolio was called “win-

ners” and comprised 35 stocks with the best performance. The

other portfolio was called “losers” and comprised 35 stocks

with the worst performance. The accumulated returns of these

two portfolios over the next three years were then examined.

Losers were found to greatly outperform winners. Behavioral

finance can provide a feasible explanation for this phenomenon.

Investors usually overestimate the value of winners and under-

estimate the value of losers, resulting in mispricing. When mis-

pricing is corrected after a period of time, the accumulated

returns of losers would be greater than that of winners.In this

paper, an ANAR-TGARCH model is adopted to test overreac-

tion or underreaction in the Chinese stock market. A series of

robust tests were conducted on the underreaction or overreac-

tion of investors by taking run length, abnormality degree, time

scale, size, sector, style, and market cycle into account. Wald

coefficients tests are then used to compare autocorrelation in-

tensities. The empirical results in this paper could help inves-

Y. FANG

tors adopt a suitable investment strategy.

Data, Models and General Empirical Results

In this section, we use daily returns in the Shanghai Compos-

ite Index, denoted by t. The value of is calculated ac-

cording to the following formula,

ln ln

rPP





, (1)

where is the daily closing price of the Shanghai Composite

Index.

The sample period is from January 2, 2001 to January 21,

2013. The sample size is 2917.

All data in this paper are derived from the Wind Financial

Terminal.

In this paper, an ANAR-TGARCH model is adopted to test

overreaction or underreaction in the Chinese stock market. The

mean equation is a first-order asymmetric autoregressive model

(ANAR), denoted by









11 11

ttttt

rIrr Irr





 

  



, (2)

and the volatility equation is a TGARCH(1,1) model, denoted





22 2

111

tttt

wI 2



 



 



(3)

Random error is assumed to follow the general error distribu-

tion (GED). Coefficient estimates are shown in Table 1, where

“*” represents the significant level of .1, “**” represents the

significant level of .05, and “***” represents the significant level

of .01 (the same below).

As shown in Table 1, both the means and volatilities of daily

returns of the Shanghai Composite Index present a significant

asymmetric pattern. Notably,



is significantly greater than 0.

Moreover,



is significantly less than 0. From the statistical

point of view, when the return at time t-1 is conditionally posi-

tive, the return at time t would present a significant positive

first-order autocorrelation. When the return at time t-1 is condi-

tionally negative, the return at time t would present a significant

negative first-order autocorrelation. From the behavioral point

of view, investors underreact to good news and overreact to bad

news.

The empirical results above can provide a significance refer-

ence with regard to which type of investment strategy to adopt.

When the previous period return is conditionally positive, one

could adopt a tendency strategy. When the previous period

return is conditionally negative, one could adopt a contrarian

strategy.

Table 1.

Coefficient estimates of the ANAR-TGARCH model for daily returns

of Shanghai Composite Index.

Coefficient Estimate P value of z-test



.071478 .0027***



−.069902 .0048***

w .000004 .0007***



.046011 .0001***



.037920 .0059***



.920696 .0000***

Furthermore, the Wald coefficients test is used to test the null

hypothesis that







 and the P value is .9633, which

shows that the first-order positive autocorrelation intensity

when the previous period return is conditionally positive does

not differ from the first-order negative autocorrelation intensity

when the previous period return is conditionally negative.

Next, we examine how the length of the return run affects the

validity of the above investment strategies. Setting the volatility

equation similar to (3), we consider the following two mean

equations,



11 1

00,1,,

tttitj t

rIrrIr jir





 



 

,

(4)



11 1

00,1,,

tttitj t

rIrrIr jir



 



 

.

(5)

The coefficient estimates of the two models above are shown

in Table 2. The results indicate that investors underreact to

good news and overreact to bad news only when the conditional

run length is relatively short. A shorter run length entails a

more remarkable first-order autocorrelation of return. In addi-

tion, the Wald test results, which are not listed in Table 2, il-

lustrate that the intensity of first-order autocorrelation of return

has nothing to do with the conditional run length.

At the end of this section, we examine how the degree of

abnormal returns affects the validity of the above investment

strategies. Setting volatility equation similar to (3), we consider

the following two mean equations,

 





 



111 1

ttt ttt

tt ttt

rIrr IErVarrrr

Ir ErVarrr













 

 ,

(6)

 





 



111 1

00 2

tttttt

tt ttt

rIrr IrErVarrr

Ir ErVarrre













 

 

(7)

The coefficient estimates of the two models above are shown

in Table 3. Investors overreact to bad news both when the con-

ditional return is normally and abnormally negative. The sig-

nificance of the first-order negative autocorrelation when the

conditional return is normally negative is greater than that when

the conditional return is abnormally negative, but no significant

difference is observed between the strengths of autocorrelation.

When the conditional return is normally positive, the first-order

positive autocorrelation is significant, but when the conditional

return is abnormally positive, the first-order positive autocorre-

lation is insignificant.

Robust Tests

Tests on Time Scale

In this section, we use the weekly and monthly returns of the

Shanghai Composite Index to test overreaction or underreaction

in the Chinese stock market, setting the mean and volatility

equation similar to (2) and (3) (the same below).

The coefficient estimates are shown in Table 4. The results

indicate that within the weekly timescale, investors do not sig-

nificantly underreact to good news or overreact to bad news. In

Open Access

Y. FANG

Open Access 73

Table 2.

Coefficient estimates of ANAR-TGARCH model for daily returns of Shanghai Composite Index with a consideration for conditional run length.

Equation (4) Equation (5)

Coefficient Estimate P value of z-test Coefficient Estimate P value of z-test



.071336 .0026***



−.070442 .0041***



−.090512 .0094*** 1



.111062 .0009***



−.088421 .0634* 2



.026338 .5340



.090333 .2724



.075712 .3345



−.165965 .0940* 4



.047697 .6512



.180070 .1775



.199883 .2348



−.081290 .5742 6



.307624 .1308



−.391777 .2408 7



−.192091 .5421



−.474708 .5323 8



.510290 .3957



−.363655 .8584

w .000003 .0009*** w .000004 .0006***



.045303 .0001***



.045735 .0001***



.036155 .0083***



.038621 .0060***



.922762 .0000***



.920068 .0000***

Table 3.

Coefficient estimates of the ANAR-TGARCH model for daily returns of Shanghai Composite Index with consideration for conditional abnormality

degree.

Equation (6) Equation (7)

Coefficient Estimate P value of z-test Coefficient Estimate P value of z-test



.071624 .0026***



−.069828 .0049***



−.049303 .0936* 1



.076686 .0055***



−.138544 .0028*** 2



.034994 0.4624

w .000004 .0007*** w .000004 .0007***



.045387 .0001***



.046174 .0001***



.037406 .0061***



.038009 .0057***



.921573 .0000***



.920490 .0000***

null hypothesis P value of Wald test

Table 4.

Coefficient estimates of ANAR-TGARCH model for weekly and monthly returns of THE Shanghai Composite Index.

Weekly returns Monthly returns

Sample period March 9, 2001 to January 25, 2013 January, 2001 to December, 2012

Sample size 599 144

Coefficient Estimate P value of z-test Estimate P value of z-test



.072910 .2498 .279506 .0291**



.041852 .4641 −.149887 .0000***

w .000025 .0590* .007757 .0003***



.048138 .0373** .331250 .1916



.028244 .2521 −.391770 .1240



.917706 .0000*** −.309830 .3107

Y. FANG

addition, volatilities do not present a significant asymmetric

pattern. Within the monthly timescale, investors significantly

underreact to good news and overreact to bad news. However,

volatilities still do not present a significant asymmetric pattern.

Furthermore, the Wald coefficients test is used to test the null

hypothesis that





 and the P value is .3171, which show

that the first-order positive autocorrelation intensity when the

previous period return is conditionally positive does not differ

from the first-order negative autocorrelation intensity when the

previous period return is conditionally negative.

Tests on Size

In this section, we examine how the size of the stock affects

the overreaction and underreaction of investors. The daily re-

turns of the CNI Large, Mid, and Small Cap Index issued by

the Shenzhen Stock Exchange are used. The sample period is

from February 16, 2005 to January 28, 2013. The sample size is

1937.

Coefficient estimates are shown in Table 5. The results indi-

cate that regardless of the size of the stock, investors signifi-

cantly exhibit underreaction to good news and overreaction to

bad news. However, volatilities do not present a significant

asymmetric pattern.

Longitudinal comparison results indicate that, for a large cap,

the first-order positive autocorrelation intensity when the pre-

vious period return is conditionally positive does not differ

from the first-order negative autocorrelation intensity when the

previous period return is conditionally negative. For the mid

and small cap, however, the first-order positive autocorrelation

intensity when the previous period return is conditionally posi-

tive is greater than the first-order negative autocorrelation in-

tensity when the previous period return is conditionally nega-

tive. The transverse comparison results indicate that, when the

previous period return is conditionally positive, the first-order

positive autocorrelation intensity of the mid cap is similar to

that of the small cap but greater than that of the large cap.

Moreover, when the previous period return is conditionally

negative, the first-order negative autocorrelation intensities of

the large, mid, and small caps do not differ.

The above longitudinal and transverse comparison results

can be directly observed from Figure 1.

Tests on Sector

In this section, we examine how the sector of the stock af-

fects the overreaction or underreaction of investors. The daily

returns of the CNI Sector Indices issued by the Shenzhen Stock

-0.15

-0.1

-0.05

0.05

0.1

0.15

0.2

0.25

0.3

lar

e ca

mid ca

small ca

first-order positive autocorrelation when the previous period return is condiontally positive

first-order negative autocorrelation when the previous period return is condiontally negative

Figure 1.

Autocorrelation intensities of large, mid, and small cap.

Table 5.

Coefficient estimates of ANAR-TGARCH model for daily returns of

CNI Large, Mid, and Small Cap Index.

Large cap

Coefficient Estimate P value of z-test



.092523 .0026***



−.096853 .0017***

w .000002 .0289**



.041968 .0004***



.006879 .5837



.948251 .0000***

Mid cap

Coefficient Estimate P value of z-test



.205111 .0000***



−.078101 .0093***

w .000006 .0043**



.059151 .0007***



.005264 .7677



.924150 .0000***

Small cap

Coefficient Estimate P value of z-test



.234120 .0000***



−.068504 .0223**

w .000009 .0016**



.068911 .0010***



.005448 .7931



.909103 .0000***

Wald test

Longitudinal comparison Transverse comparison

Null hypothesisP value Null hypothesis P value







 .9206 12



 .0136**







 .0040*** 13



 .0019***







 .0002*** 23



 .5200



 .6721



 .4415



 .7191

Exchange are used. The sample period is from January 3, 2003

to January 28, 2013. The sample size is 2444.

Coefficient estimates are shown in Table 6, in which Wald

coefficients tests results are not listed. The results indicate that

whatever the sector of the stock, volatilities do not present a

significant asymmetric pattern.

Apart from stocks from the financial sector, investors sig-

nificantly show underreaction to good news. Autocorrelation

Open Access

Y. FANG

Table 6.

Coefficient estimates of ANAR-TGARCH model for daily returns of

CNI Sector Indices.

Energy Materials

Coefficient Estimate P value of

z-test Estimate P value of

z-test



.053524 .0493** .132106 .0000***



−.049932 .0796* −.033213 .2433

w .000003 .0282** .000003 .0141**



.046084 .0000*** .057802 .0000***



.008909 .4614 .005327 0.6786



.944255 .0000*** .933158 .0000***

Industrial Consumer discretionary

Coefficient Estimate P value of

z-test Estimate P value of

z-test



.129285 .0000*** .134604 .0000***



−.045449 .0937* −.037186 .1738

w .000003 .0081*** .000003 .0063***



.050122 .0001*** .056480 .0000***



.012899 .3496 .007006 .6213



.934946 .0000*** .931492 .0000***

Consumer staples Health care

Coefficient Estimate P value of

z-test Estimate P value of

z-test



.157876 .0000*** .140169 .0000***



−.008658 .7602 .033508 .2098

w .000003 .0035*** .000003 .0077***



.081883 .0000*** .076072 .0000***



−.006091 .7201 −.017324 .2929



.912163 .0000*** .924587 .0000***

Financial information technology

Coefficient Estimate P value of

z-test estimate P value of

z-test



.038696 0.1749 .134857 .0000***



−.078657 .0064*** −.033056 .2215

w .000002 .0296** .000008 .0019***



.036239 .0001*** .067122 .0000***



.006602 .5226 −.000960 .9521



.955134 .0000*** .916598 .0000***

Telecommunication

services Utilities

Coefficient Estimate P value of

z-test Estimate P value of

z-test



.081796 .0047*** .080563 .0042***



−.030607 .2581 −.031382 .2468

w .000005 .0086*** .000002 .0088***



.057181 .0000*** .055550 .0000***



−.003283 .8166 .002466 .8544



.933169 .0000*** .935295 .0000***

intensities in the energy, telecommunication services, and utili-

ties sectors are equal. Autocorrelation intensities in the materi-

als, industrial, consumer discretionary, consumer staples, health

care, and information technology sectors are likewise equal.

The autocorrelation intensities in the former three sectors is

greater than those in the latter six sectors.

Investors significantly overreact to bad news only in the en-

ergy, industrial, and financial sectors. The significance of the

financial sector is greater than that of the energy and industrial,

but the autocorrelation intensities do not differ.

Investors exhibit both underreaction to good news and over-

reaction to bad news only in the energy and industrial sectors.

For the industrial sector, the first-order positive autocorrelation

intensity when the previous period return is conditionally posi-

tive is greater than the first-order negative autocorrelation in-

tensity when the previous period return is conditionally nega-

tive. For the energy sector, the first-order positive autocorrela-

tion intensity when the previous period return is conditionally

positive does not differ from the first-order negative autocorre-

lation intensity when the previous period return is conditionally

negative.

Tests on Styles

In this section, we examine how the style of the stock affects

the overreaction or underreaction of investors. The daily returns

of the CNI Growth and Value Index issued by the Shenzhen

Stock Exchange are used. The sample period is from January 3,

2003 to January 28, 2013. The sample size is 2444.

Coefficient estimates are shown in Table 7. The results indi-

Table 7.

Coefficient estimates of ANAR-TGARCH model for daily returns of

CNI Growth and Value Index.

Growth index

Coefficient Estimate P value of z-test



.117944 .0000***



−.063427 .0243**

w .000003 .0105**



.044699 .0001***



.017845 .1720



.938243 .0000***

Value index

Coefficient Estimate P value of z-test



.071920 .0088***



−.089074 .0012***

w .000002 .0135**



.047957 .0000***



.004711 .7051



.943149 .0000***

Wald test

Longitudinal comparison Transverse comparison

Null hypothesis P value Null hypothesis P value







 .1655 12



 .2304







 .6580 12



 .5556

Open Access 75

Y. FANG

Open Access

cate that regardless of the style of the stock, investors signifi-

cantly underreact to good news and overreact to bad news, but

volatilities do not present a significant asymmetric pattern.

overreaction or underreaction in the Chinese stock market.

The results of empirical tests based on daily returns indicate

that when the return at time t − 1 is conditionally positive, the

return at time t would present a significant positive first-order

autocorrelation. Moreover, when the return at time t − 1 is con-

ditionally negative, the return at time t would present a signifi-

cant negative first-order autocorrelation. From the behavioral

point of view, investors underreact to good news and overreact

to bad news.

A significant difference in autocorrelation intensity was not

observed in both longitudinal and transverse comparisons.

Tests on Market Cycle

In this section, we examine how the market cycle affects the

overreaction or underreaction of investors. The daily returns of

the Shanghai Composite Index are used. The bull market sam-

ple period is from August 7, 2006 to October 16, 2007. The

sample size is 289. In this period of 14 months, the Shanghai

Composite Index rose from 1547 points to 6992 points, or

293.69%. The bear market sample period is from June 13, 2001

to June 3, 2005. The sample size is 957. In this period of 48

months, the Shanghai Composite Index fell from 2242 points to

1014 points, or 293.69%.

We then conduct a series of robust tests on the underreaction

or overreaction of investors with regard to run length, abnor-

mality degree, time scale, size, sector, style, and market cycle.

Wald coefficients tests are used to compare the autocorrelation

intensities.

The empirical results in this paper could provide significant

reference for investors to adopt a suitable investment strategy.

Acknowledgments

Coefficient estimates are shown in Table 8. The results indi-

cate that within the bull market cycle, investors significantly

underreact to good news and overreact to bad news, but volatil-

ities do not present a significant asymmetric pattern. Further-

more, the P value of Wald coefficients is .0000, which indicates

that the first-order positive autocorrelation intensity when the

previous period return is conditionally positive is less than the

first-order negative autocorrelation intensity when the previous

period return is conditionally negative. Within the bear market

cycle, investors do not significantly underreact to good news

and overreact to bad news, and volatilities do not present a si-

gnificant asymmetric pattern.

This work is supported by the National Natural Science

Foundation of China through Grant No. 71171133.

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Table 8.

Coefficient estimates of ANAR-TGARCH model for daily returns

under various market cycles.

Bull market

Coefficient Estimate P value of z-test



.325701 .0000***



−.543874 .0000***

w .000187 .0011***



−.154632 .0298**



.550322 .0214**



.325373 .1168

Bear market

Coefficient Estimate P value of z-test



−.005410 .8963



−.023766 .6078

w .000008 .0369**



.019217 .3057



.149326 .0005***



.867080 .0000***

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