the impact of investor sentiment on excess returns

Available online at ijims.ms.tku.edu.tw/list.asp

International Journal of Information and Management Sciences

21 (2010), 13-28

The Impact of Investor Sentiment on Excess Returns:

A Taiwan Stock Market Case

Wu-Jen Chuang Liang-Yuh Ouyang

Department of Banking and Finance Department of Management Sciences

Tamkang University and Decision Making

R.O.C. Tamkang University

R.O.C.Wen-Chen Lo

Graduate Institute of Management Sciences

Tamkang University

R.O.C.

Abstract

In this paper, we use a proxy for investor sentiment and employ a generalized autore-

gressive conditional heteroskedasticity in mean (GARCH-M) model to show the impact of

investor sentiment on excess returns in Taiwan stock market. Firstly, the evidences suggest

that the change in trading volume is a suitable proxy for investor sentiment. Furthermore,

the conditional volatility and excess returns have a negative and significant relationship. We

argue that the irrational sentiment has influence on stock valuations.

Keywords: Trading Volume, Investor Sentiment, Excess Returns.

1. Introduction

Theoretically, investors are thought to be rational under the efficient market hypoth-

esis (EMH). Under EMH, investors are assumed to be rational and therefore to value

securities rationally. Even if some investors trade irrationally, they would trade in a

random way, and their irrational trading can be cancelled out by other different and

uncorrelated irrational trading.

Even though the EMH has dominated the field of finance for years, it still faces

many challenges, such as the big market crash on October 17 of 1987 in U.S.A. and the

irrational pricing of Internet stocks in 1990s. Many evidences indicate that irrational

behavior has an influence on security prices and it is deserved to observe thereafter.

Received October 2008; Revised May 2009; Accepted July 2009.

14 International Journal of Information and Management Sciences, Vol. 21, No. 1, March, 2010

In this paper, we find that irrational behavior has effects on security prices. First, we

develop a proxy for the unpredictable investor beliefs. And then, we employ a generalized

autoregressive conditional heteroskedasticity in mean (GARCH-M) model (Bollerslev [3,

4]; Engle et al.[14]) to test the relation between investor sentiment and excess returns in

Taiwan stock market.

The remainder of the study is organized as follows. In section 2, we discuss related

literature. In section 3, we present our methodology. In section 4, we show and interpret

our empirical results. Finally, in section 5, we summarize our conclusion and provide a

discussion of the implication.

2. Related Literature

2.1. Irrational investors’ behavior

Many empirical results show that the irrational investor behavior not only exists

in the stock market but also has significant influences on the formation of prices. In

addition, many studies argue the importance of investor sentiment in the stock market

and provide an interpretation of the influence of the sentiment beliefs on the formation of

stocks price. For instance, De Long et al. [12] propose a model to prove that noise traders

have influences on price formation. They name the risk resulting from noise traders as

“noise trader risk”. Noise trader risk is assumed to be market-wide and it has an influence

on the stock market. Most importantly, their findings validate the hypothesis that noise

traders may have a higher average return than rational investors.

De Bondt and Thaler [11] document overconfidence evidences in the stock market.

They compare the performance of two groups of companies: extreme losers and extreme

winners. The former group had poor performance in past periods, whilst the latter had

good profit. Because of irrational beliefs, investors predict that extreme winners are still

good in the future and overvalue them. Similarly, investors undervalue extreme losers.

De Bondt and Thaler [11] find that the returns of previous extreme losers are higher

than those of previous extreme winners.

Investors have a tendency to adjust their beliefs to the most recent data and to make

decision based on information they have at the present time. They also extrapolate past

experiences into future. Basu [2] provides evidences on this phenomenon. When investors

are pessimistic about the stocks characterized by series of earnings lower than expected,

they do not invest in them. As a result, such stocks have lower price earning (P/E)

ratio. As soon as the earnings increase, the prices of the stocks with extremely low

P/E ratios undergo a correction higher than the ones with extremely high P/E ratios.

And hence, low P/E stocks exhibit higher returns. The studies of Fama and French [15]

and Lakonishok et al. [20] support the result that low market-to-book ratio stocks have

bigger expected returns than high market-to-book ratio stocks. Such phenomena show

that investors usually make investment decisions based on their beliefs. Variables easy

to measure can be defined in order to describe investor’s behavior.

Furthermore, optimism is another psychological behavior that can have effects on the

formation of stock prices. The optimists believe that they have the ability to predict stock

Fluid Model Driven by an M/M/1/N Queue with Single Exponential Vacation 15

prices and to make decisions depending on their intuitions. In addition, optimistic beliefs

cause investors underestimate risk. During the late 1990’s investors were overoptimistic

about the prospects of Internet companies. Thaler [33] estimates that the intrinsic values

of Internet stocks are only about fifty percent of their market values. The evidence shows

that irrational investors involved in high risks because of their cognitive misperceptions.

Moreover, there are other irrational investment phenomena in the stock market. For

example, Shefrin and Statman [28] interpret that investors usually avoid selling stocks of

which prices are lower than their costs, so that they do not feel regret. Odean [27] also

presents that due to regret aversion, investors are reluctant to realize loss.

The argument of De Long et al. [12] supports the hypothesis that the uncertain

nature of noise trader beliefs leads rational investors to limit their positions while trading

against noise traders to avoid loss. Noise traders take the risk that they create and earn

higher returns than rational arbitragers. Furthermore they conclude that the presence of

noise traders can be detected through an excess of volatility of the prices of risky assets.

2.2. Proxy for investor sentiment

As mentioned above, several prior studies have stated that uncertain belief in sen-

timent causes higher risks in the stock market and hence gives rise to higher returns.

Recently, several researches attempt to find a proxy for the unpredictable investor beliefs.

Lee et al. [21] consider the fluctuations in the discount on closed-end funds as a proxy

for investor sentiment. Neal and Wheatley [25] examine the level of discount on closed-

end funds, the ratio of odd-lot sales to purchase, and the net mutual fund redemptions

to measure the investment behavior. Lee et al. [23] use the sentiment index provided by

Investors’ Intelligence of New Rochelle in New York as a proxy for investor sentiment.

Investors’ Intelligence takes a poll of 135 investment advisory services every week and

produces three numbers– bullish, bearish and correction. Bullish is the percentage of

investment advisors recommending investors to buy stocks. Bearish is the percentage

of those predicting a bear market. Correction is the percentage of expecting a market

correction1.

In addition, Brown and Cliff [5] examine several proxies for investor sentiment in-

cluding closed-end fund discount, the net flow of funds into mutual funds, the percentage

of mutual fund assets held as cash, and the number of IPOs during the month, the first-

day return on IPOs during the month, and the bull-bear spread. They also conclude

sentiment affects assets valuation. Tetlock [32] examines the interactions between media

content and the stock market by constructing a measure of media content corresponding

to negative investor sentiment. He finds high media pessimism inducing stock prices

downwards. Besides, Edmans et al. [13] investigate some important sports games and

find a significant loss effect of games on stock market. They show that the stock market

can react to a sudden change in investor mood.

1. The investment index is also used as a contrary indicator. According to the study of Colby and Meyers [9],when the bullish sentiment index is 37.5%, a bull market is forthcoming and when the bullish index is 78.2%, abear market is imminent. Accordingly, investors buy stocks when the bullish index is low, and sell stocks when itis high.


Even though different proxies for investor sentiment have been used in various em-

pirical studies, they all have demonstrated significant effects on stock price formation.

In this study, we try to construct a proxy reflecting investor sentiment and investigate

its effect in Taiwan stock market.

2.3. Trading volume and investor sentiment

Lee and Swaminathan [22] demonstrate that investor expectations affect not only

the return but also the trading activity of the stock. They point out that past trading

volume can be used as a proxy for measuring the fluctuations in investor sentiment. When

most investors think companies are good to invest, they buy stocks, and the trading

volume of those stocks goes higher. And when most investors consider companies are

bad, they sell or stop buying stocks, the trading volume of those stocks would be lower.

Thus trading volume can reflect investors’ expectations. They also discover that trading

volume seems to provide information about investors’ misperception of future earnings.

The information content of trading volume reflects something about relative under- or

over-valuation of stocks. They propose the momentum life cycle (MLC) to imply that

trading volume should be correlated with value (or glamour) characteristics. According to

the MLC, trading volume is an important empirical link between intermediate-horizon

momentum and long-horizon return reversal. Investors would buy the securities with

good prospects. If more and more investors extrapolate good news into future, they

tend to overvalue these firms and to invest in them. Their irrational beliefs thus increase

trading volume. On the other hand, investors would be reluctant to buy the securities

with bad news. If investors believe that the bad news would last for a long time, they tend

to undervalue these firms. And thus their irrational behavior decreases trading volume.

Hence, the change in trading volume can reflect investors’ irrational expectations to some

extent.

Shiller [30] also proposes the feedback loop theory to explain the relationships among

stock returns, investor sentiment, and trading volume during a stock market cycle. At

first, when investors are encouraged by the past prices increases, they bid up stock prices

further and earn positive returns, thereby strengthening their confidence and inducing

more investors to do the same. When the process repeats itself, the speculative bubble

develops. As the speculative bubble takes place, high stock prices are sustained by

investors’ irrational enthusiasm rather than by their intrinsic values.

However, the irrational speculative bubble can not last forever. When the bubbles

reach a certain level, investors would undergo a sudden change in their beliefs, and thus

causing the bubble to bust. And yet, there is no apparent reason for the sudden bursts

of bubbles. Hart and Tauman [17] state that such sudden changes in behavior may result

from endogenous information process which is not observable.

The feedback loop also occurs in a downward side. The initial decline in stock prices

discourages investors. As investors reduce their holdings, stock prices decline further.

At the time when the bubbles burst, the market experiences both a high volatility and a

high trading volume because of the existence of noises in investors’ demand. However, as


the downward correction process continues, market trading volume keeps shrinking due

to the loss aversion of some investors not willing to sell stocks to avoid regret. Prices

are also declining until at a certain point where the downward correction completes.

The situation where the market reaches its trough and at the same time the investors

feel extremely pessimistic is called the positive bubbles. Unlike the downward process

of a sudden burst of speculative bubbles, the positive bubbles will probably not reverse

instantaneously its upward path.

In conclusion, Lee and Swaminathan [22] find trading volume contains some informa-

tion about investors’ expectation and also link to intermediate-horizon price momentum

and long-horizon price reversal, which resulting from investors’ overconfidence bias and

conservatism bias (Daniel et al. [10], Barberis et al. [1]). With the feedback loop theory,

Shiller [30] explains the relationships among stock returns, investor sentiment, and trad-

ing volume during a stock market cycle. Even in Taiwan, Chuang and Chuang [6] find

trading volume contains many information by discovering warrants issuance in Taiwan

stock market. Based upon arguments above, we postulate that change in trading volume

can reflect fluctuations in investor sentiment.

3. Sample and Methodology

In this section, we will illustrate the proxy that represents investor sentiment and

specify a model suitable for describing the relationships between excess returns and

conditional volatility in the Taiwan stock market.

3.1. Sample period and market return proxies

The sample period of our study covers from January 4, 1990 to December 31, 2004

with a total of 779 weekly observations. The market index, Taiwan Stock Exchange Cap-

italization Weighted Stock Index (TAIEX), is used to evaluate the overall performance

of Taiwan stock market. TAIEX is the value-weighted index including all listed stocks.

The data for TAIEX and the trading volume are from the Securities and Futures Insti-

tute. The commercial paper rate, obtaining from the Taiwan Economic Journal (TEJ)

data bank, is used as a variable for the risk-free interest rate to obtain the weekly excess

returns.

3.2. Sentiment proxy

The sentiment proxy used in this study is the change in trading volume2. The rela-

tionship between the trading volume and investor sentiment can be illustrated through

the time series of the market index and the trading volume as shown in Figure 1 and Fig-

ure 2, respectively. The market index and the trading volume exhibit a strong positive

relationship3. At the tops of the market, the trading volume reaches its highest levels.

And around the troughs of the market, it obtains the lowest levels. The trading volume


Figure 1: Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) from January4, 1990 to December 31, 2004 (779 weekly observations).

declines during the periods of correction and increases as the market index goes up.

3.3. Hypothesis

Moreover, based upon findings of Lee and Swaminathan [22] and Shiller [30], high

trading volume implies that investors are optimistic about the stock or the market, and

conversely, low trading volume indicates that investors are pessimistic. That is, the

change of trading volume can represent the movement in the investor sentiment. A

positive change in the trading volume indicates a bullish change in investor sentiment,

while a negative change in volume indicates a bearish change in sentiment. That is, when

the market is going upward, investor sentiment shifts toward bullish; when the market

index is going down, investor sentiment shifts toward bearish. Moreover, the more the

changes in investor sentiment, the higher the excess returns. We will adopt the above

hypothesis and test its validity.

3.4. The model

In this paper, at first we attempt to construct a proxy for the unpredictable investor

beliefs. And then we want to examine the unpredictable investor beliefs can affect stock

valuation. The GARCH model is useful to find out the volatility in financial market and

2. We compute the change in trading volume by average weekly trading volume.3. The correlation coefficient between the market index and the trading volume is 0.7413. Both are stationary

time series.


Figure 2: The Trading volume of Taiwan Stock Exchange Capitalization Weighted Stock Index(TAIEX) from January 4, 1990 to December 31, 2004 (779 weekly observations).

there are some studies concerning Taiwan financial market (Lai et al. [19]; Ni and Wu,

[26] ). We employ a GARCH-M model to test whether the relationship between investor

sentiment and excess returns is validated in the Taiwan stock market.

Lee et al. [23] employ a GARCH-M model to show that there are some relationships

among market volatility, excess returns, and investor sentiment. There are some main

results in their study. First, they find that the investor sentiment is a significant factor

in explaining the excess returns and the volatility of stocks. Second, the greater the

magnitude of the shifts in the sentiment is, the more the impacts on the conditional

volatility of returns and expected returns. Finally, bullish and bearish shifts in the

sentiment have significant influences on excess returns and volatility. That is, investor

sentiment is a priced factor on stock returns. The results consist with arguments of De

Long et al. [12]. Irrational investors can cause an excess of volatility of the prices of risky

assets and gain higher returns.

We modify the model proposed by Lee et al. [23]. The model specification is as

follows4:

Rt − Rft = γ0 + γ1St + γ2 log(ht) + γ3Augt + εt (1)

ht = α0 + α1ε2t−1 + α2ε

2t−1It−1 + β1ht−1 + φ1(St−1)

2Dt−1 + φ2(St−1)2(1 − Dt−1)

+φ3Rft + ut (2)

4. Lee et al. [23] test excess returns of Dow Jones Industrial Average (DJIA), Standard and Poos’s 500(S&P500), and NASDAQ with sentiment index of Investors’ Intelligence. In our study, we use change in tradingvolume as sentiment index in equation (1).


where εt ∼ N(0, ht) and ut is a random error.

In equation (1), the mean equation, Rt is the weekly return on the Taiwan market

index5. The excess returns of the market index are obtained by subtracting the market

return (Rt) by the risk-free rate (Rft). St, the change in trading volume, as explained

above, is used as the proxy for investor sentiment6. ht is the conditional variance of

the market excess returns and appears in the logarithmic form in the mean equation to

capture the trade-off effect between risk and returns.

A seasonal dummy (Aug) for the month of August is also included in equation (1).

The companies in the Taiwan stock market tend to pay stock dividends instead of cash

dividends to their stockholders. When those stock dividends go public, investors are

likely to sell them and to realize gains. The result of this behavior is to depress the

stock prices. From 1990 to 2004, among 4,256 times of stock dividend distributions,

there are 696 times stock dividend released in August which accounts for 16.32% of the

total distributions.7 In the mean time, the average distribution per month is 8.33%.8

The statistics shows that the percentage of stock dividends going public in August is

higher than the average. It indicates that the stock prices should decline in the month

of August. That is, we expect there is negative relationship between returns and August

effect.

In financial markets, January effect is well known by investors. Lee et al. [23] doc-

ument that there were January effect for Dow Jones Industrial Average (DJIA) from

January 5, 1973 to October 6, 1995, and for NASDAQ from May 25, 1984 to October

6, 1995. For the Taiwan stock market, some studies (Chiou and Hwang [7]; Lee and Hu

[24]) show that January effect does exist. However, Hwang and Guo [18] indicate that

any consistent and long term seasonal effects, including the January effect, do not exist in

the Taiwan stock market. Chuang and Lai[8] investigate several factors have significant

effect on Taiwan stock market from 1992 to 2006 and January effect only shows lower

explanatory power on stock returns. In addition, Shyu and Liou[31] indicate the January

effect seems to be weaker because of higher proportion of institutional holdings. We try

to include the January effect in our model but the results are insignificant. Moreover,

we find that when the seasonal dummy (AUG) is excluded, the mean equation loses its

descriptive power. However, when it is included, the model becomes well defined.

In equation (2), the variance equation, a GARCH (1, 1) model, which incorporates

the asymmetric or leverage effects, is specified. The value of the dummy variable It−1

equals one when bad news occurs in the preceding period (εt−1 < 0), and zero otherwise.

We expect α2 to be positive as indicated by Glosten et al. [16] to show an asymmetric

effect of a higher volatility resulting from bad news than from good news.

Furthermore, in equation (2), we recognize the effect of shifts and magnitude in

investor sentiment on the volatility. The dummy variable Dt−1 equals one when there is

5. We construct the weekly rate of return on the index as Rt = ln(MIt/MIt−1), where MIt is ending weeklymarket index at time t.

6. St = V OLt − V OLt−1, where V OLt is average weekly trading volume at time t. Hence, St represents thechange in trading volume at time t.

7. The data is from Taiwan Economic Journal (TEJ) data bank.8. The average probability is equal to 8.33% (=1/12).


Figure 3: The Excess Returns of TAIEX from January 4, 1990 to December 31, 2004.

a bullish shift in investor sentiment (St−1 > 0) and zero otherwise. Thus, φ1 represents

the impact of bullish shift in investor sentiment on the volatility and φ2 is the impact of

a bearish shift on the volatility. The asymmetric impacts of investor sentiment on the

volatility can thus be observed.

Finally, the risk-free rate variable is included in the variance equation to capture the

effect of inflation on the volatility as suggested by Lee et al. [23].

4. The Empirical Results

4.1. Summary statistics

The time series of the excess returns and the sentiment proxy for the Taiwan stock

market are shown in Figure 3 and Figure 4, respectively. The sample statistics of these

two series are tabulated in Table 1. During the period of investigation, the average of

weekly excess returns is -5.67% with a maximum return of 15.42%, and a minimum -

34.89%. The sentiment proxy has a negative average value indicating a negative investor

sentiment for the sample period. It seems to show that there is on average bearish shifts

in investor sentiment, and market participants gain negative excess returns.

As we have hypothesized in section 3.3, when the market index is going down,

investor sentiment shifts toward bearish. Investors become more conservative and as a

result the market trading volume decreases. When the market index goes downward,

investors get negative returns and become more pessimistic because they tend to keep

under-cost stocks to avoid regret (Shefrin and Statman [28], Odean [27]). Table 1 exhibits

the implication similar to our hypotheses. Hence, it is reasonable to assume that there is

a connection among the change in trading volume, sentiment proxy, and excess returns.


Figure 4: The Sentiment Proxy of TAIEX from January 4, 1990 to December 31, 2004.

4.2. Estimated results

The estimated results of the four different GARCH-M models are shown in Table

2.9 We employ alternative forms of sentiment proxy into the model and then find which

may be a better proxy for investor sentiment. The base model does not include the

effect of sentiment proxy. Model 1 uses the change in trading volume in current period

(St) and the model 2 considers the change in trading volume of previous period (St−1)

as the sentiment proxy, while the model 3 and model 4 take the percentage change in

trading volume of the current period (%St) and of previous period (%St−1) respectively

to consider the effect of investor sentiment.10

The estimated coefficients of the sentiment proxy (γ1) are significant in the model 1

and 3, but not in the model 2 and 4. The results suggest that contemporary sentiment

proxy has better explanatory power in excess return and conditional volatility. That is,

investors consider more recent information to make investing decisions. Furthermore,

the model 1 with St as the sentiment proxy seems to be more suitable to explain the

relationships among excess returns, investor sentiment, and volatility. Compared with

other models, most estimated parameters of the model 1 are significant at 5% level, no

significant serial correlation remained and all of the estimated GARCH coefficients are

significant.

Lee and Swaminathan [22] indicate that trading volume provides information about

the degree of investors’ favoritism or neglect, and the change in trading volume gives

most predictive power, rather than the lagged volume. Our results are consistent with

their findings. The change in trading volume documents more convincing evidences on

9. The model is estimated by using EViews 5.1. software package. The estimation method is the maximumlikelihood method with Marquardt iterative algorithm.

10. St−1 = V OLt−1 − V OLt−2; %St = ln(V OLt/V OLt−1); %St−1 = ln(V OLt−1/V OLt−2).


Table 1: Summary statistics of excess returns and sentiment proxy.

Excess returnsSentiment proxy (St)(10 million NT dollar)

Mean -0.0567 -0.0115Standard deviation 0.0545 2.1406Min -0.3489 -9.5155Max 0.1542 8.5324Skewness -0.6576 0.3291Kurtosis 6.1230 4.9121Jarque-Bera 371.2898 132.2232(P-value) (0.0000) (0.0000)

the excess returns. In stock markets, the change in trading volume is a popular market

indicator. Trading volume always signals stock prices. Investors observe the most recent

changes in trading volume to make their investment decisions. As a result, the change

in trading volume at the current period (St) can reflect more useful information.

We summarize some findings from the model 1 of Table 2 as follows. First, the

estimated coefficient for the time-invariant long term average excess returns γ0 is negative

and significant. The results are consistent with Table 1 which indicates that excess

returns for Taiwan stock market has a negative average during the sample period.

Second, the investor sentiment has a positive and significant influence on excess

returns. Consistent with our mention in section 3.3, positive change in the trading volume

indicates bullish shift in investor sentiment and a negative change in volume is bearish

shift. That is, when investors are optimistic about the market, they gain higher returns;

when investors are pessimistic about the market, they earn lower returns. Lee et al. [23]

report the similar findings. They also find that there is a positive correlation between

excess returns and changes in sentiment in DJIA, S&P500, and NASDAQ. Moreover,

our results confirm the validity of the hypothesis that the more the changes in investor

sentiment, the higher the excess returns on the considered period.

Third, the estimated coefficient for the time-variant excess returns γ2 indicates that

there is a negative and significant relationship between the conditional volatility and

time-varying portion of excess returns. γ2 is a measure of the risk-return tradeoff. This

result seems to contradict the CAPM, but consists with previous finding of Glosten et

al. [16] and Lee et al.[23]. They argue that investors are rewarded by taking reasonable

amount of risk, but are hurt by taking high level of risk. Based upon conventional CAPM,

investors earn higher return by taking more systematic risk, but not the idiosyncratic

risk. Only if the noise trader risk is the systematic risk, investor can receive rewards for

taking such risk. Our results imply that the volatility resulting from investor sentiment

should be the unsystematic risk, not market risk.

Fourth, all of estimated GARCH coefficients are significant. α2 is positive and

significant. The results reveal there is leverage effect between positive and negative

shock. And which confirms the bad news cause higher conditional volatility. The result

is consistent with the finding of Glosten et al. [16].


Table 2: Investor sentiment, excess returns, and conditional volatility.

ParametersBase model(without St)

Model 1(with St)

Model 2(with St−1)

Model 3(with %St)

Model 4(with %St−1)

γ0 0.2141*** -0.0949*** 0.2102*** 0.2174*** -0.8972***γ1 ——— 0.0089*** - 0.0006 0.0762*** -0.0018γ2 0.0425*** -0.0061** 0.0419*** 0.0407*** -0.1344***γ3 -0.0055 -0.0084 -0.0005 -0.0028 -0.0039α0 0.0008*** 0.0012*** 0.0007*** 0.0005*** 0.0001***α1 0.0253 ** 0.1398*** 0.0359*** 0.0010 0.0006α2 0.0575** 0.1731** 0.0463*** 0.0563*** 0.0027***β1 0.7805*** 0.4545*** 0.7804*** 0.8152*** 0.9009***φ1 0.00001 -0.00001 0.0000 0.0007*** -0.0003***φ2 -0.00001 -0.00004*** -0.0000 -0.0006*** 0.0004***φ3 -0.0077*** -0.0061*** -0.0077*** -0.0049*** 0.0015***

Log-likelihood 1305.32 1304.45 1304.71 1435.32 1365.70LB Q-Statistic 2.7932 1.2272 2.4614 1.3738 28.3626

P-value (0.0254) (0.2978) (0.0040) (0.2413) (0.0000)

*, **, *** denotes coefficient estimates significant at 10%, 5%, and 1% level, respectively.The base model does not include the effect of sentiment proxy. Model 1 uses the changein trading volume in current period (St) to consider the effect of sentiment index. Model2 takes the change in trading volume of previous period (St−1) to consider the effect ofinvestor sentiment. Model 3 takes the percentage change in trading volume of currentperiod (%St) to consider the effect of sentiment. Model 4 employs the percentage changein trading volume of previous period (%St−1) to consider the effect of investor sentiment.

Furthermore, the coefficient φ1 measures the bullish magnitude in investor sentiment

and the coefficient φ2 is for the bearish magnitude in investor sentiment. The components

of bullish and bearish magnitude in sentiment consider the lagged investor sentiment,

∆St−1 . Even in the model 2 and model 4, lagged sentiment proxies in the mean equation

are not significant, they are important to form the market’s conditional volatility. Our

results find that only bearish magnitude in sentiment has significant and negative effect

on conditional volatility and excess return. That implies volatility is influenced by the

magnitude of lagged bearish sentiment. When the magnitude of lagged bearish sentiment

increases, the market’s conditional volatility gets lower. However, there is no significant

finding for bullish magnitude in investor sentiment. Based upon results of Lee et al. [23],

bullish and bearish shifts in investor sentiment have an asymmetric impact on conditional

volatility. Investors buy stocks when they are optimistic about the stock market. They

would buy the same stocks at roughly the same time or imitate their judgment with

others (Shiller [29]). Consequently, the trading volume of the stock market increases

along with a rising volatility and stock prices rise at the same time. On the other hand,

when investors are pessimistic about the market during the period of the downward

correction, some investors decide not to sell stocks to avoid realizing loss, and some

decide not to buy any stocks until the price correction completes. Thus, the trading


volume of stock market decreases with a declining volatility and stock prices fall. The

empirical results are consistent with the arguments of Shiller [30]

Finally, based upon the finding of Lee et al. [23], the risk-free rate exhibits positive

influence on volatility. However, Glosten et al. [16] state when the inflation rates are

higher in the future, the volatility is general greater. Our results show the risk-free rate

has negative and significant impact on the volatility. The reason might be there is no

high inflation rate in the sample period. Especially after year 2000, the interest rate gets

lower and the economy suffers from the deflation, so we find negative relationship be-

tween the risk-free rate and conditional volatility. Overall, our empirical results support

the sentiment proxy provides significant effects on excess returns and the formation of

conditional volatility.

4.3. Robustness check over subperiods

In this section we examine the robustness of our results. We divide the whole sample

period into two subperiods. Subperiod I is from January 4, 1990 to July 27, 1996 and

Subperiod II is from July 29, 1996 to December 31, 2004. For each subperiod, we do the

same procedures as we do for the whole sample period, running all of the Models. The

results are presented in Table 3.

From Table 3, in each subperiod we also find the contemporary sentiment proxy

has better explanatory power in excess return and conditional volatility, not the lagged

sentiment proxy. Moreover, in subperiod I, Model 1 with St as the sentiment proxy also

shows better explanatory among excess returns, investor sentiment, and volatility. Most

results consist with the whole sample period. However, bullish magnitude in sentiment

shows significant and positive effect on conditional volatility and excess return. This

finding is consistent with the argument of section 4.2. Moreover, the risk-free rate shows

positive and significant impact on the volatility. In the subperiod I, the interest rate is

higher, so the results do not contradict to Glosten et al. [16]. In subperid II, there is

no well-specified model with sentiment proxy. During this subperiod, the stock market

experiences the Internet bubble and market crash, which causes unusual volatility. This

is a possible reason we can not find well-specified model with sentiment proxy.

5. Concluding Remarks

In this paper, we use the change in trading volume as a proxy for unpredictable

investor beliefs and model the impact of investor sentiment on excess returns. First,

we find the change in trading volume can be used as a proxy for investor sentiment.

The change in trading volume can provide some information about investors’ irrational

behavior. When investor sentiment is bullish, the trading volume increases. On the other

hand, bearish sentiment induces investors to sell stocks at first and then decrease trading

to avoid loss realization afterwards. In addition, we find the change in trading volume

at current period has more persuading power for investor sentiment.

Secondly, a GARCH-M model with asymmetric effects is suitable to explain the re-

lationship among the investor sentiment, excess returns, and the volatility in the Taiwan


Table 3: Robustness of Investor sentiment, excess returns, and conditional volatility over subpe-riods.

Base model(without St)

Model 1(with St)

Model 2(with St−1)

Model 3(with %St)

Model 4(with %St−1)

Panel A: Subperiod I (January 4, 1990 ∼ July 27, 1996)γ0 0.2186*** -0.1575*** -0.2395*** -0.2168*** -0.2024***γ1 ——— 0.0158*** -0.0009 0.0753*** -0.0033γ2 -0.0240*** -0.0136*** -0.0274*** -0.0227*** -0.0214***γ3 -0.0223** -0.0203*** -0.0224** -0.0134* -0.0223**α0 -0.0004*** -0.0002*** -0.0005*** -0.0007*** -0.0006***α1 0.0115 -0.0493*** 0.0367 0.1520*** 0.0824**α2 0.0411 0.0416*** 0.0175 -0.0438 0.0086β1 0.9219*** 1.0222*** 0.8728*** 0.6308*** 0.8509***φ1 0.00004 0.00002*** 0.00001 -0.0013*** -0.0001φ2 -0.00004 0.0000 -0.000002 0.0013 0.0008φ3 0.0070*** 0.0019* 0.0096*** 0.0161*** 0.0113***

Log-likelihood 554.69 613.38 554.51 611.78 554.57

Panel B: Subperiod II (July 29, 1996 ∼ December 31, 2004)γ0 2.0169 -1.3630* 0.0482** -0.9374*** 2.2255***γ1 ——— 0.0078*** -0.0004 0.0819*** -0.0055γ2 0.3241 -0.1989* 0.0145*** -0.1319*** 0.3577***γ3 -0.0026 0.0021 -0.0004 0.0029 0.0011α0 0.0004* 0.0004** 0.0007*** 0.0001*** 0.0002***α1 0.0020 0.0021 0.0528 -0.0017 0.0015α2 -0.0001 -0.0070 0.1263** -0.0051 -0.0023β1 0.8012*** 0.5954*** 0.7086*** 0.8941*** 0.8803***φ1 0.0000 -0.00001* 0.0000 -0.0004*** 0.0001**φ2 -0.0000 0.00001 0.0000 0.0002 0.0002***φ3 -0.0012 0.0029 -0.0090*** -0.0010*** -0.0006**

Log-likelihood 814.84 894.72 763.64 915.35 820.10

*, **, *** denotes coefficient estimates significant at 10%, 5%, and 1% level, respectively.The base model does not include the effect of sentiment proxy. Model 1 uses the changein trading volume in current period (St) to consider the effect of sentiment index. Model2 takes the change in trading volume of previous period (St−1) to consider the effect ofinvestor sentiment. Model 3 takes the percentage change in trading volume of currentperiod (%St) to consider the effect of investor sentiment. Model 4 employs the percentagechange in trading volume of previous period (%St−1) to consider the effect of investorsentiment.

stock market. Investor sentiment has a positive and significant influence on excess re-

turns. Shifts in the beliefs of investor sentiment have significant effects on the market

volatility. The results show that noise traders do have influences on the price formation

of stocks and the market volatility.

Finally, the conditional volatility and excess returns have a negative and significant

relationship. The irrational sentiment affects on stock valuations. However, the volatility

resulting from investor sentiment gives rise to idiosyncratic risk, not systematic risk.


Our results imply that the volatility resulting from investor sentiment should be the

unsystematic risk, not market risk.

In conclusion, our study shows that investor sentiment affects stock prices in Taiwan

stock market. In Taiwan stock market, the change in trading volume is a common market

indicator for investors. Investors usually observe the change in trading volume first and

then make their investment decisions. Hence, the change in trading volume can reflect

some degree of investors’ expectations in Taiwan stock market. Indeed, our findings

highlight the importance of investor sentiment on the prices and volatility formation.

Nevertheless, questions remain as to make investment strategies based upon investor

sentiment. We hope to address such topic in our ongoing research.

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Authors’ Information

Wu-Jen Chuang is currently the associate professor in Department of Banking and Finance, TamkangUniversity, Taiwan, R.O.C.. His research interests are Financial Markets, Econometrics, and Banking.

Department of Banking and Finance, Tamkang University, Tamsui, Taipei, Taiwan 251, R.O.C.

E-mail: [email protected] TEL: +886-2-2621-5656 ext. 3335

Liang-Yuh Ouyang is a Professor in the Department of Management Sciences and Decision Making atTamkang University in Taiwan. He earned his Ph.D. in Management Sciences from Tamkang University.His research interests are in the field of Production/Inventory Control, Probability and Statistics.

Department of Management Sciences and Decision Making, Tamkang University, Tamsui, Taipei 251,Tai-wan, R.O.C.


Wen-Chen Lo is currently the Ph.D. candidate in Graduate Institute of Management Sciences, TamkangUniversity, Taiwan, R.O.C. and the Instructor of Department of Finance in St. John’s University, Taiwan,R.O.C.. Her research interests are Financial Markets and Behavioral Finance.

Department of Finance, St. John’s Universiry, Taiwan, R.O.C.


the impact of investor sentiment on excess returns

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