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Noise trading and stock market volatility
J. of Multi. Fin. Manag. 17 (2007) 231–243
Noise trading and stock market volatility Rahul Verma a,∗ , Priti Verma b,1 a
College of Business, University of Houston-Downtown, One Main Street, Houston, TX 77002, United States b College of Business, Texas A&M University, Kingsville, TX 78363, United States Received 16 June 2005; accepted 31 October 2006 Available online 14 December 2006
Abstract We investigate the relative effects of fundamental and noise trading on the formation of conditional volatility. We find significant positive (negative) effects of investor sentiments on stock returns (volatilities) for both individual and institutional investors. There are greater positive effects of rational sentiments on stock returns than irrational sentiments. Conversely, there are significant (insignificant) negative effects of irrational (rational) sentiments on volatility. Also, we find asymmetric (symmetric) spillover effects of irrational (rational) bullish and bearish sentiments on the stock market. Evidence in favor of irrational sentiments is consistent with the view that investor error is a significant determinant of stock volatilities. © 2006 Elsevier B.V. All rights reserved. JEL classification: G12; G14 Keywords: Volatility; Investor sentiment
1. Introduction Noise trader models in finance imply that subsets of investors often do not make investment decisions based on a company’s fundamentals and are capable of affecting stock prices by way of unpredictable changes in their sentiments. Much previous research provides a theoretical framework describing the relevance of investor sentiments in asset pricing. Most notable for this paper is the research of DeLong, Shleifer, Summers, and Waldmann (DSSW) (1990). Their creation of the noise trader model lead to further studies which provide evidence in favor of strong co∗ 1
Corresponding author. Tel.: +1 713 221 8590; fax: +1 713 226 5238. E-mail addresses: [email protected] (R. Verma), [email protected] (P. Verma). Tel: +1 361 593 2355; fax: +1 361 593 3912.
1042-444X/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mulfin.2006.10.003
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movements between investor sentiment and the stock market returns recognizing the existence of individual investor sentiments, as well as institutional investor sentiments. Previous research focuses on the mean of stock returns while less attention is given to the impact of sentiments on the formation of conditional volatility. Specifically, the existing tests focus primarily on first moment contemporaneous correlations between investor sentiments and stock returns. No analysis is done to investigate the manner in which noise trading by individual and institutional investors may affect expected return through its effect on the market’s formation of risk. The question arises: to what extent do individual and institutional investor sentiments impact stock market volatilities? Moreover, if such relationships do exist, are the effects driven by rational risk factors or noise? Answers to these questions are important in order to better understand how noise trader risk is priced in the U.S. market. In this study, we investigate the relative effects of fundamental and noise trading on the formation of conditional volatility as suggested by DSSW (1990). Specifically, we make the following contribution to the extant literature: first, unlike previous studies which examine the relationship between sentiments and the mean of stock returns, we test the impact of individual and institutional investor sentiments on the stock market volatility; second, unlike previous studies which treat sentiments as fully irrational exuberance, we focus on both the rational and noise (irrational) components of investor sentiments and explore their relative effects on the volatility of stock returns; third, we investigate asymmetrical behavior of investor sentiments and stock volatility by differentiating between bullish and bearish sentiments. We estimate a set of multivariate EGARCH models and find significant positive (negative) effects of investor sentiments on stock market returns (volatilities) for both individual and institutional investors. Unlike previous studies which conjecture investor sentiments as fully irrational, we find that the individual and institutional investor sentiments are driven by both rational and irrational factors. We find that rational sentiments have greater positive effects on stock returns than the irrational sentiments for both classes of investors. In the case of volatility we find significant negative effect of only irrational sentiments. Consistent with the behavioral theories, we find greater effect of irrational bullish sentiments than irrational bearish sentiments on stock market for both individuals and institutions. However, in the case of rational sentiments, we do not find the existence of such asymmetric effects. This remainder of this paper is organized as follows. Section 2 presents the model while Section 3 presents the data. In Section 4, we provide estimation results and Section 5 concludes. 2. Model The impact of noise trading as suggested by DSSW (1990) is due to the interaction of four effects of investor sentiments on stock returns and volatility. The first effect is due to the trading by bullish or bearish investors which takes the price away from the fundamental value. The second effect is the result of the adjustment in the market risk due to the changes in noise traders’ demand of stocks based on their sentiments. Consequently, in the case of bullish sentiments, when the first effect is more than the second effect, the mean return is higher and vice versa. On the other hand, in the case of bearish sentiments, the mean return is always lower while both the effects build up. Specifically, these two effects capture the short-run effect of noise trading on excess returns due to the contemporaneous changes in investor sentiments. The third effect captures the fluctuations in stock prices due to the variations of noise traders’ misperceptions about the risk. When a majority of noise traders are more bullish (bearish) than the average, they bid up (down) the stock price. Consequently, the more numerous the noise traders are
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relative to informed investors, the more volatile the stock prices. The fourth effect captures the deviations of stock prices from its fundamental value due to the fact that the average misperceptions of noise traders associated with shifts in sentiments is not zero. Increase in such misperceptions about stock’s risk increases the uncertainty and reduces the position of informed investors. Consequently, the returns are higher when this effect is more than the third effect and vice versa. Specifically, these two effects capture the long run impact of noise trading on excess returns associated with the impact of the shift in sentiments on the formation of future volatilities of stock returns. Brown and Cliff (2004) suggest that both individuals and institutions may have different systematic misevaluation. For example, they may respond differently to signals when forming their sentiments. Although both individuals and institutions display significant sentiments, only institutions have enough market power to affect prices. Specifically, shocks originating from sentiments of one class of investors not considered in an analysis might mistakenly be seen as a disturbance originating from sentiments of another class of investors that are included in the analysis. Therefore, it is important to jointly model the sentiments of both individual and institutional investors to avoid misspecification. We test the impact of noise trading associated with the shifts in investor sentiments in two steps. First, we examine the relative effect of individual and institutional investor sentiments on the formation of conditional volatility as suggested by DSSW (1990). Second, we investigate whether the effects of sentiments on stock volatility are driven by rational risk factors, or noise as suggested by Brown and Cliff (2006) and Shleifer and Summers (1990). Since studies such as Brown and Cliff (2004, 2006) and Lee et al. (2002) suggest that stock market returns and investor sentiments may act as a system, we choose the multivariate version of Nelson’s (1991) Exponential Generalized ARCH (EGARCH) model. Specifically, we employ multivariate version of Nelson’s EGARCH extended by Koutmos and Booth (1995) and Koutmos (1998) so that we can also investigate asymmetric effects of bullish and bearish sentiments on stock volatilities.2 The Vector Autoregressive (VAR) model (Sims, 1980) in the mean equation is appropriate when estimating unrestricted reduced-form equations with an uniform set of dependent variables as regressors. The model is also appropriate for analyzing our postulated relationships because it does not impose a priori restrictions on the structure of the system and can be viewed as a flexible approximation to the reduced form of the correctly specified but unknown model of true economic nature. The mean equation takes the following: Ri,t = βi,0 +
3
βi,j Rj,t−1 + εi,t ;
i, j = 1, 2, 3; i = jx
(1)
j=1
In the above model, Rit is the excess return on the market index (i = 1), individual investor sentiments (i = 2), and institutional investor sentiments (i = 3). εi,t is the residual. βi,0 and βi,j are the parameters to be estimated. Specifically, the parameter βi,j captures the degree of mean spillover effects across sentiments and returns. A significant βi,j coefficient would mean that variable j leads variable i, or equivalently, that current j can be used to predict future i.3 2 Nelson’s EGARCH model is a univariate one and it only considers the asymmetric impacts of positive and negative innovations of a previous period on current conditional volatility. It does not examine the asymmetric impact of positive and negative innovations of one variable on the volatility of other variable. 3 Since the purpose of the paper is not to analyze how market return and volatility are affected by its past innovations, but rather to investigate the spillover effects between sentiments and market volatility, we have specified the constraint i = j.
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To model the conditional variances, we propose the following trivariate EGARCH (Koutmos and Booth, 1995; Koutmos, 1998): ⎫ ⎧ 3 ⎬ ⎨ 2 2 ) ; i, j = 1, 2, 3; i = j (2) σi,t = exp αi,0 + αi,j fj (zj,t−1 ) + γi ln(σi,t−1 ⎭ ⎩ j=1
fj (Zj,t−1 ) = (|Zj,t−1 | − E|Zj,t−1 | + δj Zj,t−1 ),
j = 1, 2, 3
(3)
where Zj,t−1 is the standardized residual at time t − 1 which is defined as εj,t−1 /σ j,t−1, and E|Zj,t−1 | is the expected value of Zj,t−1 . The parameters αi,j captures the volatility spillover among the markets, i.e., the effect of innovations from variable j to variable i. For example, a significant α1,2 would mean that volatility in individual investor sentiments would significantly affect volatility of returns. The asymmetric effect of negative innovations to positive innovations on conditional volatility is measured by the ratio |−1 + δj |/(1 + δj |). A negative value of δj will lead to a larger value of the ratio indicating that negative innovations will have greater effects on conditional volatility than positive innovations. A significant positive (negative) αi,j coupled with a negative (positive) δj implies that negative (positive) innovations in variable j have a higher impact on volatility of variable i than positive (negative) innovations. This implies that the volatility spillover mechanism is asymmetric. Following Bollerslev (1990), we have assumed a time invariant correlation matrix while estimating the multivariate EGARCH model. Our approach is similar to studies employing multivariate EGARCH models such as Koutmos and Booth (1995), Koutmos (1998), and So (2001). Under this specification, the covariance is equal to the product of the standard deviations (σ i,j,t = ρi,j σ i,t σ j,t for i, j = 1,2,3; i = j). This specification reduces the number of parameters and makes the estimation more tractable. Next, we decompose investor sentiments into noise (irrational) and fundamental (rational) components since sentiments could reflect investors’ biases such as excessive optimism or pessimism. Excessive optimism (pessimism) may drive prices above (below) their intrinsic values. Since sentiments partially contain rational expectations based on risk factors (Brown and Cliff, 2004; Hirshleifer, 2001; Shleifer and Summers, 1990), it is quite possible that stock returns and volatility are affected by both fundamental and noise components of sentiments. When an investor is bullish or bearish, their behavior could be a rational reflection of a future period’s expectation or irrational enthusiasm or a combination of both. Therefore, it is important to control for this information sentiments may contain about rational factors. Accordingly, we model rational and irrational effects of fundamentals and noise, respectively on sentiments of individual and institutional investors as under: Senttit = λi0 + λij
J
fundjit + ξit
(4)
j=1
where λi0 is constant, λij are the parameters to be estimated, and ξ it are the random error terms. Specifically, Sentt1t and Sentt2t represent the sentiments of individual and institutional investors, respectively at time t. Fundjt is the set of fundamentals representing rational expectations based on risk factors that have been shown to carry non-redundant information in conditional asset pricing literature. The fitted values of Eq. (4) capture the rational components of individual and institutional investor sentiments (i.e., Sentˆt1t and Sentˆt2t ). On the other hand, the residuals could capture the irrational components of individual and institutional investor sentiments (i.e. ξ 1t and ξ 2t ).
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Next, we analyze the extent to which the mean and the conditional variance of stock returns are affected by investor-sentiment induced noise or fundamental trading. We include the rational and noise component of investor sentiments in the five variable VAR-EGARCH model as under: Ri,t = βi,0 +
5
βi,j Rj,t−1 + εi,t ;
i, j = 1, 2, 3, 4, 5; i = j
(5)
j=1
2 σi,t
⎫ ⎧ 5 ⎬ ⎨ 2 αi,j fj (zj,t−1 ) + γi ln(σi,t−1 ) ; = exp αi,0 + ⎭ ⎩
i, j = 1, 2, 3, 4, 5; i = j
(6)
j=1
and fj (Zj,t−1 ) = (|Zj,t−1 | − E|Zj,t−1 | + δj Zj,t−1 ),
j = 1, 2, 3, 4, 5
(7)
In the above model, Rit is the excess return on the market index (i = 1), rational individual investor sentiments (i = 2), irrational individual investor sentiments (i = 3), rational institutional investor sentiments (i = 4), and irrational institutional investor sentiments (i = 5). εi,t is the residual. βi,0 and βi,j are the parameters to be estimated. Specifically, the parameter βi,j captures the degree of mean spillover effects across sentiments and returns. The parameters αi,j captures the volatility spillover among the markets, i.e., the effect of innovations from variable j to variable i. A significant positive αi,j coupled with a negative δj implies that volatility spillover mechanism is asymmetric. 3. Data We obtain all data in monthly intervals from October 1988 to April 2004. Our choice of individual investor sentiment index is based on Brown and Cliff (2004), Fisher and Statman (2000), and DeBondt (1993), which use the survey data of American Association of Individual Investor. Our choice of institutional investor sentiment index is based on Brown and Cliff (2004, 2006), Lee et al. (2002), Clarke and Statman (1998), and Solt and Statman (1988) which use the survey data of Investors Intelligence. We employ DJIA and S&P500 to characterize the overall performance of the market. The continuously compounded returns for both indicators are obtained from the Datastream. We include the following variables as fundamentals shown to carry non-redundant information in the asset pricing literature: economic growth, short-term interest rates, economic risk premia, future economic expectations variables, business conditions, dividend yield, inflation, excess returns on market portfolio, premium on portfolio of small stocks relative to large stocks (SMB), premium on portfolio of high book/market stocks relative to low book/market stocks (HML), momentum factor (UMD), and currency fluctuation. The data on economic growth, business conditions, and inflation are obtained from Datastream; short-term interest rates, economic risk premium, future economic variables, and currency fluctuations are obtained from Federal Reserve Bank of St. Louis; dividend yield and excess return on market portfolio are from CRSP; SMB, HML, and UMD are from Kenneth French Data Library at Tuck School of Business, Dartmouth College. Table 1 reports the descriptive statistics of the above-mentioned variables. The mean of Sntt1 and Sntt2 are approximately 11% and 9%, respectively. This suggests both individual and institutional investors are bullish during most of the sample period. Interestingly, individual investors are more bullish than institutional investors.
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Table 1 Descriptive statistics
Sentt1 Sentt2 DJIA S&P500 IIP T30 T90-T30 B10 T30 Baa-Aaa Div INF Rm SMB HML UMD USD
Mean
Median
Maximum
Minimum
Standard deviation
Skewness
Kurtosis
0.1143 0.0896 0.0102 0.0096 0.0026 0.0043 0.0004 0.0071 0.0079 0.0127 0.0026 0.0031 −0.0012 0.0024 1.1658 0.4233
0.1200 0.1100 0.0137 0.0147 0.0032 0.0041 0.0004 0.0078 0.0074 0.0153 0.0023 0.0077 −0.0028 0.0009 1.3200 0.3270
0.5100 0.3640 0.0913 0.1011 0.0199 0.0080 0.0017 0.0549 0.0144 0.1141 0.0103 0.0994 0.2138 0.1367 18.2100 4.2894
−0.3500 −0.3420 −0.1177 −0.1094 −0.0121 0.0021 −0.0003 −0.0440 0.0053 −0.1437 −0.0012 −0.1655 −0.1626 −0.1205 −25.1300 −3.1701
0.1760 0.1413 0.0394 0.0389 0.0052 0.0013 0.0004 0.0181 0.0018 0.0408 0.0021 0.0414 0.0382 0.0363 4.5224 1.1005
−0.0863 −0.5373 −0.5175 −0.5279 −0.1011 0.4793 0.8185 −0.0562 1.0835 −0.4639 0.9335 −0.7543 1.0244 0.4417 −0.7366 0.3533
2.6626 2.9513 3.5256 3.5607 3.2547 2.9139 3.7719 3.1558 4.3342 3.9027 4.3616 4.3240 11.0803 5.3273 11.7315 4.3973
The variables are individual investor sentiments (Sentt1 ), institutional investor sentiments (Sentt2 ), returns on Dow Jones Industrial Average (DJIA), returns on S&P500 (S&P500), economic growth (IIP), short-term interest rates (T30), economic risk premiums (T90-T30), future economic variables (B10-T30), business conditions (Baa-Aaa), dividend yield (Div.), inflation (INF), excess returns on market portfolio (Rm ), premium on portfolio of small stocks relative to large stocks (SMB), premium on portfolio of high book/market stocks relative to low book/market stocks (HML), momentum factors (UMD), and currency fluctuations (USD).
The mean returns of DJIA and S&P500 are approximately 1.02% and 0.95%, respectively. This suggests large capitalization stocks provide less returns than the overall market. The two sentiments have higher standard deviations than those of stock market indexes, suggesting investor sentiments are highly volatile during the sample period. 4. Estimation results In accordance with Eqs. (1)–(3) we estimate a set of multivariate EGARCH models for both DJIA and S&P500. Table 2 (model 1) reports the estimated coefficients for the mean and the variance equations for both market indicators. There is substantial evidence of multidirectional lead-lag relationships among individual and institutional investor sentiments and stock returns. The significant positive coefficients β1,2 , and β1,3 for both the market indicators are consistent with the view that both individual and institutional investor sentiments play a significant role in determining stock prices in the U.S. market. The significant negative coefficients for α1,2 and α1,3 suggest volatility spillovers from both individual and institutional investor sentiments into stock market volatility. This inverse relationship is consistent with previous findings of negative price of time varying risk (Glosten et al., 1993; De Santis and Gerard, 1997). Specifically, shifts in bullish (bearish) institutional investor sentiments may cause significant downward (upward) revisions in the volatility (Lee et al., 2002). Also, the effect of institutional investor sentiments (α1,3 ) is much higher than those of the individual investor sentiments (α1,2 ). This follows Brown and Cliff (2004) in that both individuals and institutions may have different systematic misvaluations such that they respond differently to signals in formation of their sentiments thereby causing dissimilar effects on stock
Table 2 Effects of individual and institutional investor sentiments on DJIA & S&P500 excess return and conditional volatility Model 1 (complete sample) DJIA
S&P500
0.0353***
(0.0028) (0.0184) 0.0491*** (0.0159) 0.0686*** (0.0165) 0.0655* (0.0388) 0.0302 (0.0730) 0.0302 (0.0226) 0.2005 (0.5775) 0.0715 (0.1526) −0.0014 (0.0622) 0.4523*** (0.1580) 0.9857*** (0.0239) −0.0209* (0.0123) −0.4597** (0.2209) 0.8017* (0.4582) 0.2256 (0.1577) 0.2416** (0.1221) 0.1521 (0.5054) 0.8732*** (0.0203) 0.3604*** (0.1492) 0.3083* (0.1654) 0.0423**
DJIA
0.0470***
(0.0046) (0.0226) 0.0858*** (0.0257) 0.1387*** (0.0184) 0.0619** (0.0297) 0.0739 (0.0457) 0.0402*** (0.0159) 0.2263 (0.3540) −0.0742 (0.0885) −7.3366*** (1.2162) −2.1963*** (0.8635) −3.0172** (1.2961) 0.4552* (0.2591) −0.5618*** (0.1178) 0.4124 (0.2893) 1.0721*** (0.3988) −0.0839 (0.1981) 0.1973 (0.3096) 0.5582*** (0.1024) 0.3793*** (0.1228) 0.4995 (0.5485) 0.0899***
Model 2 (recession) S&P500
0.0512***
(0.0069) (0.0191) 0.0514*** (0.0125) 0.0527** (0.0265) 0.0712* (0.0408) 0.0469 (0.0896) 0.0395* (0.0233) 0.2566 (0.6587) −0.0798 (0.1642) −0.6547 (0.6235) 0.2325*** (0.1235) 1.1589*** (0.0325) −0.0365** (0.0158) −0.4825** (0.2122) 1.2587* (0.6525) 0.2698 (0.2589) 0.3126* (0.1854) 0.2583 (0.6731) 0.9924*** (0.0568) 0.4785*** (0.1896) 0.3577** (0.1785) 0.0571***
DJIA
0.0573***
(0.0081) (0.0285) 0.0832*** (0.0278) 0.1267*** (0.0165) 0.0624* (0.0379) 0.0852 (0.0792) 0.0482* (0.0293) 0.2989 (0.3891) −0.0865 (0.0896) −0.6895 (0.6158) −0.3854* (0.2162) 15.3268* (8.6589) −0.5462* (0.3217) −0.5937* (0.3135) 1.1158** (0.5239) 0.7817 (0.4925) 1.1725 (1.6892) 0.2008 (0.6589) 0.6589*** (0.1896) 0.4127** (0.1985) 0.3258 (0.2589) 0.0876***
S&P500
0.0312***
(0.0037) (0.0165) 0.0256 (0.0163) 0.0315 (0.0263) 0.0412* (0.0272) 0.0421 (0.0776) 0.0215 (0.0298) 0.2689 (0.1954) −0.0121 (0.0111) −0.2135 (0.2589) 0.2589*** (0.1189) 0.8524*** (0.0365) −0.0181* (0.0105) −0.1136 (0.1856) 1.2189 (1.1198) 0.2119 (0.1937) 0.1193 (0.1725) 0.3125 (0.6987) 0.7145*** (0.0658) 0.2247* (0.1289) 0.2126** (0.1189) 0.0272*
0.0398*** (0.0039) 0.0346* (0.0203) 0.0393 (0.0297) 0.0876*** (0.0372) 0.0389 (0.0347) 0.0752 (0.0657) 0.0278 (0.0245) 0.2756 (0.2151) −0.0117 (0.0165) −0.1214 (0.3256) 0.3112*** (0.1258) 1.2598*** (0.0658) 0.2152* (0.1139) −0.2752 (0.1937) 1.3678 (1.2592) 0.7254 (0.4789) 0.1537 (0.3698) 0.2148 (0.2213) 0.4128** (0.1987) 0.1972** (0.9814) 0.1015 (0.1897)
Diagnostic checks: P-value statistics
LB (12) LB2 (12)
i=1
i=2
i=3
i=1
i=2
i=3
0.731 0.178
0.596 0.159
0.679 0.354
0.496 0.748
0.554 0.684
0.408 0.532
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β1,0 β1,2 β1,3 β2,0 β2,1 β2,3 β3,0 β3,1 β3,2 α1,0 α2,0 α3,0 α1,2 α1,3 α2,1 α3,1 α2,3 α3,2 δ1 δ2 δ3
Model 2 (growth)
The variables are excess return on the market index (i = 1), individual investor sentiments (i = 2), and institutional investor sentiments (i = 3). Note (*), (**), and (***) denote significance levels at the 10%, 5%, and 1%, respectively. Standard errors are in the parentheses. 237
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prices. Perhaps, although both individuals and institutions display significant sentiments, only institutions have enough market power to affect the volatilities. We investigate the possibility of asymmetric impact of the individual and institutional investor sentiments on stock market by examining the coefficients αi,j coupled with δj . Significant negative α1,2 and α13 coupled with a significant positive δ2 and δ3 imply that volatility spillover mechanism is asymmetric in both the cases. Specifically, there is greater effect of bullish than bearish investor sentiments on stock market volatility. This finding is consistent with the DHS model and other behavioral explanations (Brown and Cliff, 2006; Gervais and Odean, 2001; Wang, 2001; Hong et al., 2000) which suggest that the effect of sentiments on stock prices can be asymmetric. We also find significant parameters β2,1 and α2,1 which show that stock market returns and investor sentiments can act as a system and indicate a positive role of the stock market in the formation of individual investor sentiments. This finding suggests that individual investor sentiments show extrapolation bias to the extent that increased bullishness can be expected after a market rise and increased bearishness after a market fall (DeBondt, 1993), thereby making individuals “positive feedback traders”. This evidence is also consistent with the existence of bandwagon effect (Brown and Cliff, 2004) which states that stock returns predict future sentiments. However, in the case of institutional investor sentiments, we do not find the existence of such relationship suggesting that individuals, rather than institutions, are more likely to be positive feedback traders. Moreover, a significant α2,1 coupled with significant positive δ1 indicate the existence of asymmetric effect of stock market on individual investor sentiments. Innovations in stock market may have stronger effect on bullish sentiments during the period of growth than similar effects on the bearish sentiments during the period of decline. Lastly, we find significant α2,3 in case of DJIA while insignificant α3,2 in both the cases suggesting that that there is positive volatility spillover from the institutional to individual investor sentiments but not the other way round. This finding is consistent with the arguments of Nofsinger and Sias (1999) and Brown and Cliff (2004) which suggest that institutional investors have superior information and make up a disproportionately larger portion of the market relative to individuals. As such it is quite possible that individuals tend to follow institutional investor sentiments and not vice versa. In order to check the robustness of these results we make a distinction between the periods of growth and decline in the market. We split the sample into two periods, growth (1988–2001) and recession (2001–2004), and then re-estimate two additional models. Specifically, we estimate models 2 and 3 for the growth and recession period, respectively. The effect of individual and institutional investor sentiments on stock returns (β1,2 , β1,3 ) is significant in both the models. However, the magnitudes of these coefficients are much higher in the case of model 2. Similarly the response of market volatilities to investor sentiments (α1,2 and α1,3 ) is greater during the growth than recession period. In addition, we find significant α2,1 in model 2 and insignificant result in model 3. These findings suggest that individual investors have a greater (lesser) bandwagon effect and greater (lesser) positive feedback trading during a growth (decline) period. Similarly, the existence of asymmetry is higher in model 2 than 3. Overall, these findings indicate that the link between sentiments, market returns, and volatilities is stronger (weaker) during the phases of rally (decline) in the market. Table 4 reports the results of the residual-based diagnostic checks of multivariate EGARCH model for both DJIA and S&P500. The p values for Ljung-Box statistic for 12-order serial correlation of standardized residuals and the squared standardized residuals are insignificant in both cases. These results show that the multivariate EGARCH model can adequately describe the dynamic relationship between the three variables.
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Table 3 Effects of fundamentals on individual and institutional investor sentiments Variables
Sentt1
Sentt2
B10 Baa IIP HML INF Rm DIV SMB T30 T90 UMD USD C R2 SSR Akaike info criterion Schwarz criterion F-statistic Prob. (F-statistic)
−0.96 (0.88) −29.93*** (8.35) 1.30 (2.77) 1.44*** (0.53) −18.28*** (6.60) −6.75** (3.29) 8.32*** (3.31) 2.78*** (0.80) 7.47 (13.57) −13.11 36.71 0.00 (0.00) 0.00 (0.01) 0.29*** (0.07) 0.304 3.190 −0.839 −0.578 4.989 0.000
0.49 (0.71) −4.82 (8.27) −2.22 (2.20) 1.14*** (0.46) −8.35 (6.06) −3.60 (2.66) 4.50* (2.71) 1.99*** (0.66) −6.83 (11.51) −31.70 (31.64) 0.00 (0.00) 0.00 (0.01) 0.15** (0.07) 0.161 2.48 −1.090 −0.829 2.186 0.015
The variables are individual investor sentiments (Sentt1 ), institutional investor sentiments (Sentt2 ), economic growth (IIP), short-term interest rates (T30), economic risk premiums (T90), future economic variables (B10), business conditions (Baa), dividend yield (Div), inflation (INF), excess returns on market portfolio (Rm ), premium on portfolio of small stocks relative to large stocks (SMB), premium on portfolio of high book/market stocks relative to low book/market stocks (HML), momentum factors (UMD), and currency fluctuations (USD). Note (*), (**), and (***) denote significance levels at the 10%, 5%, and 1%, respectively. Standard errors are in the parentheses.
Since our primary focus is to analyze the relative effects of rational and irrational investor sentiments on stock market returns and volatility, we decompose the sentiment variables into rational and irrational components based on fitted and residual values of Eq. (2). Specifically, we estimate two separate ordinary least square (OLS) regressions based on Eq. (4). Table 3 reports the regression results. The individual investor sentiments (Sentt1 ) are significantly related to business conditions, inflation, dividend yield, excess returns on market, SMB, and HML. Similarly the institutional investor sentiments are significantly related to dividend yield, SMB, and HML. These results are consistent with the argument of Brown and Cliff (2006) that investor sentiments may contain a combination of both rational and irrational components and not necessarily only noise. We generate the fitted values (Sentˆtit ) and residuals (ξ it ) for each regression to compute the rational and irrational components of investor sentiments, respectively. To analyze the relative effects of rational and irrational investor sentiments on stock market returns and volatilities, as depicted in Eqs. (5)–(7), we estimate a set of multivariate EGARCH models for DJIA and S&P500. In addition to the returns on the two market indexes, we include the four new variables derived from Eq. (4) related to rational and irrational sentiments of individual and institutional investors. Table 4 reports the estimation results and diagnostics. In the mean equations there are significant positive effects of the rational individual (β1,2 ) and institutional (β1,4 ) investor sentiments on market returns. These results are consistent with our earlier findings that both individual and institutional investor sentiments significantly affect DJIA and S&P500 returns. Also, the effects of rational institutional investor sentiments are much higher than those of the rational individual investor sentiments for both the cases. Similarly the effects
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Table 4 Effects of rational and irrational sentiments of individual and institutional investors on DJIA & S&P500 excess return and conditional volatility
β1,0 β1,2 β1,3 β1,4 β1,5 β2,0 β2,1 β2,3 β2,4 β2,5 β3,0 β3,1 β3,2 β3,4 β3,5 β4,0 β4,1 β4,2 β4,3 β4,5 β5,0 β5,1 β5,2 β5,3 β5,4 α1,0 α2,0 α3,0 α4,0 α5,0 α1,2 α1,3 α1,4 α1,5 α2,1 α2,3 α2,4 α2,5 α3,1 α3,2 α3,4 α3,5 α4,1 α4,2 α4,3 α4,5 α5,1 α5,2 α5,3 α5,4
DJIA
S&P500
−0.0129 (0.0164) 0.0990** (0.0475) 0.0406 (0.0674) 0.1198*** (0.0300) −0.0311 (0.2200) 0.0967*** (0.0236) 0.6081 (16.7165) 0.0601 (1.9083) 0.0198 (6.1142) 0.0884 (2.9728) 0.0102 (0.5572) 0.0599* (0.0328) 0.0436 (5.6535) −0.0368 (11.9265) 0.0572 (8.8682) 0.0100*** (0.0027) 0.0489 (0.3829) 0.0505 (0.0921) 0.0500 (0.0491) 0.0499 (0.0934) 0.0100*** (0.0013) 0.0496 (0.2137) 0.0499 (0.0547) 0.0500** (0.2166) 0.0504 (0.1291) −0.2655 (37.9540) −4.8443 (30.4121) −1.3827 (17.0423) 0.0287 (8.6933) −0.0714 (5.3301) −0.1282 (2.3189) −0.1028* (0.0536) −0.0743 (4.4533) −0.1183* (0.0640) −6.7005 (28.4347) −0.0454 (21.7526) 0.1669 (12.1557) 0.0793 (4.7532) 1.1655** (0.5796) −0.0365 (1.4668) 0.0673 (6.9666) 0.0298 (4.5222) 0.1083 (1.2608) 0.0406 (3.6713) 0.0451 (7.0142) 0.0527 (1.0916) 0.0340 (0.0382) 0.0891 (1.6373) 0.0447 (3.4031) 0.0421 (1.3093)
0.0043 (0.0079) 0.0734** (0.0312) 0.0410* (0.0228) 0.0822*** (0.0239) 0.0509** (0.0251) 0.0711*** (0.0208) −0.0732 (0.1706) 0.0576 (0.0641) 0.3373 (0.2324) 0.0252 (0.0780) −0.0133 (0.0354) 0.1515** (0.0757) 0.1212 (0.3548) 0.0293 (0.5782) 0.0876 (0.1312) 0.0303 (0.0210) 0.1291 (0.2362) 0.1155 (0.1569) 0.0714 (0.0651) 0.0337 (0.0812) −0.0395 (0.0352) 0.8414 (0.6374) −0.5517 (0.5136) −0.1388 (0.1511) 1.0134 (0.7880) −2.7929* (1.5785) −1.1954 (1.1616) −3.1875** (1.5173) −4.6916** (2.2885) −5.6774*** (1.4504) −0.0620 (0.5628) −0.2570* (0.1475) 0.0680 (0.4954) −0.2024* (0.1220) 0.6115 (0.5715) 0.0269 (0.3158) −0.1167 (0.4919) 0.1742 (0.4583) 0.1273* (0.0713) −0.1763 (0.4964) 0.0891 (0.4613) −0.0014 (0.5071) −0.5393 (0.6255) 0.3585 (0.6186) 0.0464 (0.4399) 0.2215 (0.4600) 0.6273 (0.6381) −0.0690 (0.4169) 0.4588 (0.5384) 0.8593 (0.7413)
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Table 4 (Continued )
δ1 δ2 δ3 δ4 δ5
DJIA
S&P500
0.8949 (0.8625) 0.5272 (1.2377) 0.8603** (0.3690) 0.0998 (0.5386) 0.9975** (0.5459)
0.1036*** (0.0237) −0.0288 (0.0783) 0.1541*** (0.0468) 0.2685*** (0.0060) 0.5108* (0.2974)
Diagnostic checks: P-value statistics i=1 LB (12) LB2 (12)
0.253 0.145
i=2
i=3
i=4
i=5
i=1
i=2
i=3
i=4
i=5
0.250 0.125
0.158 0.158
0.148 0.124
0.212 0.198
0.413 0.325
0.223 0.256
0.254 0.221
0.189 0.279
0.256 0.298
The variables are excess return on the market index (i = 1), rational individual investor sentiments (i = 2), irrational individual investor sentiments (i = 3), rational institutional investor sentiments (i = 4), and irrational institutional investor sentiments (i = 5). Note (*), (**), and (***) denote significance levels at the 10%, 5%, and 1%, respectively. Standard errors are in the parentheses.
of irrational components of investor sentiments for both individuals (β1,3 ) and institutions (β1,5 ) in case of S&P500 are positive and significant. However, the effect of irrational sentiments is less than those of rational sentiments for both individual and institutional investors. These results indicate that the effect of investor sentiments on stock market returns is mainly attributed to the fundamental trading and less to the noise trading. In the variance equations, there are insignificant effects of the rational individual and institutional investor sentiments. Unlike the effects on the mean of stock market returns, the coefficients α12 and α14 are insignificant suggesting that rational sentiments does not cause a great deal of variability in stock prices. On the other hand, there are significant negative effects of irrational investor sentiments (α13 and α15 ) on stock market volatilities. The negative effect of irrational sentiments on volatility is consistent with the predictions of DSSW (1990) and other noise trader models that the effect of noise trading on expected returns is through its impact on the market’s formation of risk. Lastly, we find there are significant coefficients β3,1 and α3,1 which indicate that there are significant positive effects of stock returns and volatility in the formation of irrational sentiments of individual investors. These significant responses of irrational sentiments to stock market could explain the existence of positive feedback trading by individual investors. Conversely, there are insignificant effects of stock market returns and volatility (β5,1 and α5,1 ) in the case of rational investor sentiments. Insignificant results for rational and irrational institutional investor sentiments confirm the previous finding that institutional investors are less likely to be positive feedback traders. A significant δ1 coupled with positive α3,1 suggest greater effect of stock market innovations on bullish irrational sentiments during the period of growth than similar effects on bearish irrational sentiments during the period of decline. The P values for Ljung-Box statistic for 12-order serial correlation of standardized residuals and the squared standardized residuals show no evidence of first or second moment time dependencies in the standardized residuals. These diagnostic tests verify that the five variable multivariate EGARCH model are correctly specified. 5. Conclusion This study investigates the relative effects of fundamental and noise trading on the formation of conditional volatility of stock returns as suggested by DSSW (1990). We estimate a set of
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multivariate EGARCH model for DJIA and S&P500 returns. The first model is consistent with previous findings in that there are significant positive (negative) effects of investor sentiments on stock market returns (volatilities) for both individuals and institutions. We find these relationships to be asymmetric since there is a greater effect of bullish sentiments than bearish sentiments. The effect of the stock market on the formation of individual investor sentiments (institutional investor sentiments) is significant (insignificant). These results suggest that individuals are more likely to be positive feedback traders. We also find that individual investor sentiments react to institutional investor sentiments but not vice versa. Unlike previous studies which conjecture investor sentiments as fully irrational, we find that the individual and institutional investor sentiments are driven by both rational and irrational factors. The individual investor sentiments are significantly related to business conditions, inflation, dividend yield, excess returns on market, SMB, and HML. Similarly the institutional investor sentiments are significantly related to dividend yield, SMB, and HML. In the second model, we find that rational sentiments have greater positive effects on stock returns than the irrational sentiments for both individuals and institutions. In the case of volatility, we find significant negative effects of only the irrational component of sentiments. Consistent with behavioral theories, we find greater effects of irrational bullish sentiments than irrational bearish sentiments on the stock market for both individuals and institutions. However, in the case of rational sentiments, we do not find the existence of such asymmetric effects. Lastly, we find significant positive effects of stock returns and volatility in the formation of irrational sentiments of individual investors. These results may explain the positive feedback nature of individual investors. Evidence in favor of irrational sentiments is consistent with the view that investor error is a significant determinant of stock volatilities. The direct implication of these results is that conventional measures of temporal variation in risk omit an important source of risk: noise. Overall, the findings suggest that noise is a priced risk factor. We also find strong support for the role of economic fundamentals as determinants of stock market returns and volatility.
References Bollerslev, T., 1990. Modeling the coherence in short-run nominal exchange rates: a multivariate generalized Arch model. The Review of Economics and Statistics 72, 498–505. Brown, G.W., Cliff, M.T., 2004. Investor sentiment and the near-term stock market. Journal of Empirical Finance 11, 1–27. Brown, G.W., Cliff, M.T., 2006. Investor sentiment and asset valuation. Journal of Business, forthcoming. Clarke, R.G., Statman, M., 1998. Bullish or bearish? Financial Analysts Journal, 63–72. DeBondt, W., 1993. Betting on trends: intuitive forecasts of financial risk and return. International Journal of Forecasting 9, 355–371. DeLong, Shleifer, J., Summers, A., Waldmann, R., 1990. Noise trader risk in financial markets. Journal of Political Economy 98, 703–738. De Santis, Gerard, 1997. International asset pricing and portfolio diversification with time varying risk. Journal of Finance 52, 1881–1912. Fisher, K.L., Statman, M., 2000. Investor sentiments and stock returns. Financial Analysts Journal 56, 16–23. Gervais, S., Odean, T., 2001. Learning to be overconfident. Review of Financial Studies 14, 1–28. Glosten, Jagannathan, Runkle, 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48, 1770–1801. Hirshleifer, D., 2001. Investor psychology and asset pricing. Journal of Finance 56, 1533–1597. Hong, H., Lim, T., Stein, J.C., 2000. Bad news travels slowly: size, analysts coverage, and the profitability of momentum strategies. Journal of Finance 55, 265–292.
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Koutmos, G., Booth, G.G., 1995. Asymmetries in the conditional mean and the conditional variance: evidence from nine stock markets. Journal of Economics and Business 50, 277–290. Koutmos, G.G., 1998. Asymmetric volatility transmission in international stock markets. Journal of International Money and Finance 14, 747–762. Lee, W.Y., Jiang, C.X., Indro, D.C., 2002. Stock market volatility, excess returns, and the role of investor sentiments. Journal of Banking and Finance 26, 2277–2299. Nelson, D.B., 1991. Conditional heteroskedasticity in asset returns: a new approach. Econometrica 59, 347–370. Nofsinger, J.R., Sias, R.W., 1999. Herding and feedback trading by institutional and individual investors. Journal of Finance 6, 2263–2295. Shleifer, A., Summers, L., 1990. The noise trader approach to finance. Journal of Economic Perspectives 4 (2), 19–33. Sims, C., 1980. Macroeconomics and reality. Econometrica 48, 1–49. So, R.W., 2001. Price and volatility spillovers between interest rate and exchange value of the US dollar. Global Finance Journal 12, 95–107. Solt, M.E., Statman, M., 1988. How useful is the sentiment index? Financial Analysts Journal 43 (1), 83–95, 45–55. Wang, F.A., 2001. Overconfidence, investor sentiment, and evolution. Journal of Financial Intermediation 10, 138–170.
Noise trading and stock market volatility Rahul Verma a,∗ , Priti Verma b,1 a
College of Business, University of Houston-Downtown, One Main Street, Houston, TX 77002, United States b College of Business, Texas A&M University, Kingsville, TX 78363, United States Received 16 June 2005; accepted 31 October 2006 Available online 14 December 2006
Abstract We investigate the relative effects of fundamental and noise trading on the formation of conditional volatility. We find significant positive (negative) effects of investor sentiments on stock returns (volatilities) for both individual and institutional investors. There are greater positive effects of rational sentiments on stock returns than irrational sentiments. Conversely, there are significant (insignificant) negative effects of irrational (rational) sentiments on volatility. Also, we find asymmetric (symmetric) spillover effects of irrational (rational) bullish and bearish sentiments on the stock market. Evidence in favor of irrational sentiments is consistent with the view that investor error is a significant determinant of stock volatilities. © 2006 Elsevier B.V. All rights reserved. JEL classification: G12; G14 Keywords: Volatility; Investor sentiment
1. Introduction Noise trader models in finance imply that subsets of investors often do not make investment decisions based on a company’s fundamentals and are capable of affecting stock prices by way of unpredictable changes in their sentiments. Much previous research provides a theoretical framework describing the relevance of investor sentiments in asset pricing. Most notable for this paper is the research of DeLong, Shleifer, Summers, and Waldmann (DSSW) (1990). Their creation of the noise trader model lead to further studies which provide evidence in favor of strong co∗ 1
Corresponding author. Tel.: +1 713 221 8590; fax: +1 713 226 5238. E-mail addresses: [email protected] (R. Verma), [email protected] (P. Verma). Tel: +1 361 593 2355; fax: +1 361 593 3912.
1042-444X/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mulfin.2006.10.003
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movements between investor sentiment and the stock market returns recognizing the existence of individual investor sentiments, as well as institutional investor sentiments. Previous research focuses on the mean of stock returns while less attention is given to the impact of sentiments on the formation of conditional volatility. Specifically, the existing tests focus primarily on first moment contemporaneous correlations between investor sentiments and stock returns. No analysis is done to investigate the manner in which noise trading by individual and institutional investors may affect expected return through its effect on the market’s formation of risk. The question arises: to what extent do individual and institutional investor sentiments impact stock market volatilities? Moreover, if such relationships do exist, are the effects driven by rational risk factors or noise? Answers to these questions are important in order to better understand how noise trader risk is priced in the U.S. market. In this study, we investigate the relative effects of fundamental and noise trading on the formation of conditional volatility as suggested by DSSW (1990). Specifically, we make the following contribution to the extant literature: first, unlike previous studies which examine the relationship between sentiments and the mean of stock returns, we test the impact of individual and institutional investor sentiments on the stock market volatility; second, unlike previous studies which treat sentiments as fully irrational exuberance, we focus on both the rational and noise (irrational) components of investor sentiments and explore their relative effects on the volatility of stock returns; third, we investigate asymmetrical behavior of investor sentiments and stock volatility by differentiating between bullish and bearish sentiments. We estimate a set of multivariate EGARCH models and find significant positive (negative) effects of investor sentiments on stock market returns (volatilities) for both individual and institutional investors. Unlike previous studies which conjecture investor sentiments as fully irrational, we find that the individual and institutional investor sentiments are driven by both rational and irrational factors. We find that rational sentiments have greater positive effects on stock returns than the irrational sentiments for both classes of investors. In the case of volatility we find significant negative effect of only irrational sentiments. Consistent with the behavioral theories, we find greater effect of irrational bullish sentiments than irrational bearish sentiments on stock market for both individuals and institutions. However, in the case of rational sentiments, we do not find the existence of such asymmetric effects. This remainder of this paper is organized as follows. Section 2 presents the model while Section 3 presents the data. In Section 4, we provide estimation results and Section 5 concludes. 2. Model The impact of noise trading as suggested by DSSW (1990) is due to the interaction of four effects of investor sentiments on stock returns and volatility. The first effect is due to the trading by bullish or bearish investors which takes the price away from the fundamental value. The second effect is the result of the adjustment in the market risk due to the changes in noise traders’ demand of stocks based on their sentiments. Consequently, in the case of bullish sentiments, when the first effect is more than the second effect, the mean return is higher and vice versa. On the other hand, in the case of bearish sentiments, the mean return is always lower while both the effects build up. Specifically, these two effects capture the short-run effect of noise trading on excess returns due to the contemporaneous changes in investor sentiments. The third effect captures the fluctuations in stock prices due to the variations of noise traders’ misperceptions about the risk. When a majority of noise traders are more bullish (bearish) than the average, they bid up (down) the stock price. Consequently, the more numerous the noise traders are
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relative to informed investors, the more volatile the stock prices. The fourth effect captures the deviations of stock prices from its fundamental value due to the fact that the average misperceptions of noise traders associated with shifts in sentiments is not zero. Increase in such misperceptions about stock’s risk increases the uncertainty and reduces the position of informed investors. Consequently, the returns are higher when this effect is more than the third effect and vice versa. Specifically, these two effects capture the long run impact of noise trading on excess returns associated with the impact of the shift in sentiments on the formation of future volatilities of stock returns. Brown and Cliff (2004) suggest that both individuals and institutions may have different systematic misevaluation. For example, they may respond differently to signals when forming their sentiments. Although both individuals and institutions display significant sentiments, only institutions have enough market power to affect prices. Specifically, shocks originating from sentiments of one class of investors not considered in an analysis might mistakenly be seen as a disturbance originating from sentiments of another class of investors that are included in the analysis. Therefore, it is important to jointly model the sentiments of both individual and institutional investors to avoid misspecification. We test the impact of noise trading associated with the shifts in investor sentiments in two steps. First, we examine the relative effect of individual and institutional investor sentiments on the formation of conditional volatility as suggested by DSSW (1990). Second, we investigate whether the effects of sentiments on stock volatility are driven by rational risk factors, or noise as suggested by Brown and Cliff (2006) and Shleifer and Summers (1990). Since studies such as Brown and Cliff (2004, 2006) and Lee et al. (2002) suggest that stock market returns and investor sentiments may act as a system, we choose the multivariate version of Nelson’s (1991) Exponential Generalized ARCH (EGARCH) model. Specifically, we employ multivariate version of Nelson’s EGARCH extended by Koutmos and Booth (1995) and Koutmos (1998) so that we can also investigate asymmetric effects of bullish and bearish sentiments on stock volatilities.2 The Vector Autoregressive (VAR) model (Sims, 1980) in the mean equation is appropriate when estimating unrestricted reduced-form equations with an uniform set of dependent variables as regressors. The model is also appropriate for analyzing our postulated relationships because it does not impose a priori restrictions on the structure of the system and can be viewed as a flexible approximation to the reduced form of the correctly specified but unknown model of true economic nature. The mean equation takes the following: Ri,t = βi,0 +
3
βi,j Rj,t−1 + εi,t ;
i, j = 1, 2, 3; i = jx
(1)
j=1
In the above model, Rit is the excess return on the market index (i = 1), individual investor sentiments (i = 2), and institutional investor sentiments (i = 3). εi,t is the residual. βi,0 and βi,j are the parameters to be estimated. Specifically, the parameter βi,j captures the degree of mean spillover effects across sentiments and returns. A significant βi,j coefficient would mean that variable j leads variable i, or equivalently, that current j can be used to predict future i.3 2 Nelson’s EGARCH model is a univariate one and it only considers the asymmetric impacts of positive and negative innovations of a previous period on current conditional volatility. It does not examine the asymmetric impact of positive and negative innovations of one variable on the volatility of other variable. 3 Since the purpose of the paper is not to analyze how market return and volatility are affected by its past innovations, but rather to investigate the spillover effects between sentiments and market volatility, we have specified the constraint i = j.
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To model the conditional variances, we propose the following trivariate EGARCH (Koutmos and Booth, 1995; Koutmos, 1998): ⎫ ⎧ 3 ⎬ ⎨ 2 2 ) ; i, j = 1, 2, 3; i = j (2) σi,t = exp αi,0 + αi,j fj (zj,t−1 ) + γi ln(σi,t−1 ⎭ ⎩ j=1
fj (Zj,t−1 ) = (|Zj,t−1 | − E|Zj,t−1 | + δj Zj,t−1 ),
j = 1, 2, 3
(3)
where Zj,t−1 is the standardized residual at time t − 1 which is defined as εj,t−1 /σ j,t−1, and E|Zj,t−1 | is the expected value of Zj,t−1 . The parameters αi,j captures the volatility spillover among the markets, i.e., the effect of innovations from variable j to variable i. For example, a significant α1,2 would mean that volatility in individual investor sentiments would significantly affect volatility of returns. The asymmetric effect of negative innovations to positive innovations on conditional volatility is measured by the ratio |−1 + δj |/(1 + δj |). A negative value of δj will lead to a larger value of the ratio indicating that negative innovations will have greater effects on conditional volatility than positive innovations. A significant positive (negative) αi,j coupled with a negative (positive) δj implies that negative (positive) innovations in variable j have a higher impact on volatility of variable i than positive (negative) innovations. This implies that the volatility spillover mechanism is asymmetric. Following Bollerslev (1990), we have assumed a time invariant correlation matrix while estimating the multivariate EGARCH model. Our approach is similar to studies employing multivariate EGARCH models such as Koutmos and Booth (1995), Koutmos (1998), and So (2001). Under this specification, the covariance is equal to the product of the standard deviations (σ i,j,t = ρi,j σ i,t σ j,t for i, j = 1,2,3; i = j). This specification reduces the number of parameters and makes the estimation more tractable. Next, we decompose investor sentiments into noise (irrational) and fundamental (rational) components since sentiments could reflect investors’ biases such as excessive optimism or pessimism. Excessive optimism (pessimism) may drive prices above (below) their intrinsic values. Since sentiments partially contain rational expectations based on risk factors (Brown and Cliff, 2004; Hirshleifer, 2001; Shleifer and Summers, 1990), it is quite possible that stock returns and volatility are affected by both fundamental and noise components of sentiments. When an investor is bullish or bearish, their behavior could be a rational reflection of a future period’s expectation or irrational enthusiasm or a combination of both. Therefore, it is important to control for this information sentiments may contain about rational factors. Accordingly, we model rational and irrational effects of fundamentals and noise, respectively on sentiments of individual and institutional investors as under: Senttit = λi0 + λij
J
fundjit + ξit
(4)
j=1
where λi0 is constant, λij are the parameters to be estimated, and ξ it are the random error terms. Specifically, Sentt1t and Sentt2t represent the sentiments of individual and institutional investors, respectively at time t. Fundjt is the set of fundamentals representing rational expectations based on risk factors that have been shown to carry non-redundant information in conditional asset pricing literature. The fitted values of Eq. (4) capture the rational components of individual and institutional investor sentiments (i.e., Sentˆt1t and Sentˆt2t ). On the other hand, the residuals could capture the irrational components of individual and institutional investor sentiments (i.e. ξ 1t and ξ 2t ).
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Next, we analyze the extent to which the mean and the conditional variance of stock returns are affected by investor-sentiment induced noise or fundamental trading. We include the rational and noise component of investor sentiments in the five variable VAR-EGARCH model as under: Ri,t = βi,0 +
5
βi,j Rj,t−1 + εi,t ;
i, j = 1, 2, 3, 4, 5; i = j
(5)
j=1
2 σi,t
⎫ ⎧ 5 ⎬ ⎨ 2 αi,j fj (zj,t−1 ) + γi ln(σi,t−1 ) ; = exp αi,0 + ⎭ ⎩
i, j = 1, 2, 3, 4, 5; i = j
(6)
j=1
and fj (Zj,t−1 ) = (|Zj,t−1 | − E|Zj,t−1 | + δj Zj,t−1 ),
j = 1, 2, 3, 4, 5
(7)
In the above model, Rit is the excess return on the market index (i = 1), rational individual investor sentiments (i = 2), irrational individual investor sentiments (i = 3), rational institutional investor sentiments (i = 4), and irrational institutional investor sentiments (i = 5). εi,t is the residual. βi,0 and βi,j are the parameters to be estimated. Specifically, the parameter βi,j captures the degree of mean spillover effects across sentiments and returns. The parameters αi,j captures the volatility spillover among the markets, i.e., the effect of innovations from variable j to variable i. A significant positive αi,j coupled with a negative δj implies that volatility spillover mechanism is asymmetric. 3. Data We obtain all data in monthly intervals from October 1988 to April 2004. Our choice of individual investor sentiment index is based on Brown and Cliff (2004), Fisher and Statman (2000), and DeBondt (1993), which use the survey data of American Association of Individual Investor. Our choice of institutional investor sentiment index is based on Brown and Cliff (2004, 2006), Lee et al. (2002), Clarke and Statman (1998), and Solt and Statman (1988) which use the survey data of Investors Intelligence. We employ DJIA and S&P500 to characterize the overall performance of the market. The continuously compounded returns for both indicators are obtained from the Datastream. We include the following variables as fundamentals shown to carry non-redundant information in the asset pricing literature: economic growth, short-term interest rates, economic risk premia, future economic expectations variables, business conditions, dividend yield, inflation, excess returns on market portfolio, premium on portfolio of small stocks relative to large stocks (SMB), premium on portfolio of high book/market stocks relative to low book/market stocks (HML), momentum factor (UMD), and currency fluctuation. The data on economic growth, business conditions, and inflation are obtained from Datastream; short-term interest rates, economic risk premium, future economic variables, and currency fluctuations are obtained from Federal Reserve Bank of St. Louis; dividend yield and excess return on market portfolio are from CRSP; SMB, HML, and UMD are from Kenneth French Data Library at Tuck School of Business, Dartmouth College. Table 1 reports the descriptive statistics of the above-mentioned variables. The mean of Sntt1 and Sntt2 are approximately 11% and 9%, respectively. This suggests both individual and institutional investors are bullish during most of the sample period. Interestingly, individual investors are more bullish than institutional investors.
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Table 1 Descriptive statistics
Sentt1 Sentt2 DJIA S&P500 IIP T30 T90-T30 B10 T30 Baa-Aaa Div INF Rm SMB HML UMD USD
Mean
Median
Maximum
Minimum
Standard deviation
Skewness
Kurtosis
0.1143 0.0896 0.0102 0.0096 0.0026 0.0043 0.0004 0.0071 0.0079 0.0127 0.0026 0.0031 −0.0012 0.0024 1.1658 0.4233
0.1200 0.1100 0.0137 0.0147 0.0032 0.0041 0.0004 0.0078 0.0074 0.0153 0.0023 0.0077 −0.0028 0.0009 1.3200 0.3270
0.5100 0.3640 0.0913 0.1011 0.0199 0.0080 0.0017 0.0549 0.0144 0.1141 0.0103 0.0994 0.2138 0.1367 18.2100 4.2894
−0.3500 −0.3420 −0.1177 −0.1094 −0.0121 0.0021 −0.0003 −0.0440 0.0053 −0.1437 −0.0012 −0.1655 −0.1626 −0.1205 −25.1300 −3.1701
0.1760 0.1413 0.0394 0.0389 0.0052 0.0013 0.0004 0.0181 0.0018 0.0408 0.0021 0.0414 0.0382 0.0363 4.5224 1.1005
−0.0863 −0.5373 −0.5175 −0.5279 −0.1011 0.4793 0.8185 −0.0562 1.0835 −0.4639 0.9335 −0.7543 1.0244 0.4417 −0.7366 0.3533
2.6626 2.9513 3.5256 3.5607 3.2547 2.9139 3.7719 3.1558 4.3342 3.9027 4.3616 4.3240 11.0803 5.3273 11.7315 4.3973
The variables are individual investor sentiments (Sentt1 ), institutional investor sentiments (Sentt2 ), returns on Dow Jones Industrial Average (DJIA), returns on S&P500 (S&P500), economic growth (IIP), short-term interest rates (T30), economic risk premiums (T90-T30), future economic variables (B10-T30), business conditions (Baa-Aaa), dividend yield (Div.), inflation (INF), excess returns on market portfolio (Rm ), premium on portfolio of small stocks relative to large stocks (SMB), premium on portfolio of high book/market stocks relative to low book/market stocks (HML), momentum factors (UMD), and currency fluctuations (USD).
The mean returns of DJIA and S&P500 are approximately 1.02% and 0.95%, respectively. This suggests large capitalization stocks provide less returns than the overall market. The two sentiments have higher standard deviations than those of stock market indexes, suggesting investor sentiments are highly volatile during the sample period. 4. Estimation results In accordance with Eqs. (1)–(3) we estimate a set of multivariate EGARCH models for both DJIA and S&P500. Table 2 (model 1) reports the estimated coefficients for the mean and the variance equations for both market indicators. There is substantial evidence of multidirectional lead-lag relationships among individual and institutional investor sentiments and stock returns. The significant positive coefficients β1,2 , and β1,3 for both the market indicators are consistent with the view that both individual and institutional investor sentiments play a significant role in determining stock prices in the U.S. market. The significant negative coefficients for α1,2 and α1,3 suggest volatility spillovers from both individual and institutional investor sentiments into stock market volatility. This inverse relationship is consistent with previous findings of negative price of time varying risk (Glosten et al., 1993; De Santis and Gerard, 1997). Specifically, shifts in bullish (bearish) institutional investor sentiments may cause significant downward (upward) revisions in the volatility (Lee et al., 2002). Also, the effect of institutional investor sentiments (α1,3 ) is much higher than those of the individual investor sentiments (α1,2 ). This follows Brown and Cliff (2004) in that both individuals and institutions may have different systematic misvaluations such that they respond differently to signals in formation of their sentiments thereby causing dissimilar effects on stock
Table 2 Effects of individual and institutional investor sentiments on DJIA & S&P500 excess return and conditional volatility Model 1 (complete sample) DJIA
S&P500
0.0353***
(0.0028) (0.0184) 0.0491*** (0.0159) 0.0686*** (0.0165) 0.0655* (0.0388) 0.0302 (0.0730) 0.0302 (0.0226) 0.2005 (0.5775) 0.0715 (0.1526) −0.0014 (0.0622) 0.4523*** (0.1580) 0.9857*** (0.0239) −0.0209* (0.0123) −0.4597** (0.2209) 0.8017* (0.4582) 0.2256 (0.1577) 0.2416** (0.1221) 0.1521 (0.5054) 0.8732*** (0.0203) 0.3604*** (0.1492) 0.3083* (0.1654) 0.0423**
DJIA
0.0470***
(0.0046) (0.0226) 0.0858*** (0.0257) 0.1387*** (0.0184) 0.0619** (0.0297) 0.0739 (0.0457) 0.0402*** (0.0159) 0.2263 (0.3540) −0.0742 (0.0885) −7.3366*** (1.2162) −2.1963*** (0.8635) −3.0172** (1.2961) 0.4552* (0.2591) −0.5618*** (0.1178) 0.4124 (0.2893) 1.0721*** (0.3988) −0.0839 (0.1981) 0.1973 (0.3096) 0.5582*** (0.1024) 0.3793*** (0.1228) 0.4995 (0.5485) 0.0899***
Model 2 (recession) S&P500
0.0512***
(0.0069) (0.0191) 0.0514*** (0.0125) 0.0527** (0.0265) 0.0712* (0.0408) 0.0469 (0.0896) 0.0395* (0.0233) 0.2566 (0.6587) −0.0798 (0.1642) −0.6547 (0.6235) 0.2325*** (0.1235) 1.1589*** (0.0325) −0.0365** (0.0158) −0.4825** (0.2122) 1.2587* (0.6525) 0.2698 (0.2589) 0.3126* (0.1854) 0.2583 (0.6731) 0.9924*** (0.0568) 0.4785*** (0.1896) 0.3577** (0.1785) 0.0571***
DJIA
0.0573***
(0.0081) (0.0285) 0.0832*** (0.0278) 0.1267*** (0.0165) 0.0624* (0.0379) 0.0852 (0.0792) 0.0482* (0.0293) 0.2989 (0.3891) −0.0865 (0.0896) −0.6895 (0.6158) −0.3854* (0.2162) 15.3268* (8.6589) −0.5462* (0.3217) −0.5937* (0.3135) 1.1158** (0.5239) 0.7817 (0.4925) 1.1725 (1.6892) 0.2008 (0.6589) 0.6589*** (0.1896) 0.4127** (0.1985) 0.3258 (0.2589) 0.0876***
S&P500
0.0312***
(0.0037) (0.0165) 0.0256 (0.0163) 0.0315 (0.0263) 0.0412* (0.0272) 0.0421 (0.0776) 0.0215 (0.0298) 0.2689 (0.1954) −0.0121 (0.0111) −0.2135 (0.2589) 0.2589*** (0.1189) 0.8524*** (0.0365) −0.0181* (0.0105) −0.1136 (0.1856) 1.2189 (1.1198) 0.2119 (0.1937) 0.1193 (0.1725) 0.3125 (0.6987) 0.7145*** (0.0658) 0.2247* (0.1289) 0.2126** (0.1189) 0.0272*
0.0398*** (0.0039) 0.0346* (0.0203) 0.0393 (0.0297) 0.0876*** (0.0372) 0.0389 (0.0347) 0.0752 (0.0657) 0.0278 (0.0245) 0.2756 (0.2151) −0.0117 (0.0165) −0.1214 (0.3256) 0.3112*** (0.1258) 1.2598*** (0.0658) 0.2152* (0.1139) −0.2752 (0.1937) 1.3678 (1.2592) 0.7254 (0.4789) 0.1537 (0.3698) 0.2148 (0.2213) 0.4128** (0.1987) 0.1972** (0.9814) 0.1015 (0.1897)
Diagnostic checks: P-value statistics
LB (12) LB2 (12)
i=1
i=2
i=3
i=1
i=2
i=3
0.731 0.178
0.596 0.159
0.679 0.354
0.496 0.748
0.554 0.684
0.408 0.532
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β1,0 β1,2 β1,3 β2,0 β2,1 β2,3 β3,0 β3,1 β3,2 α1,0 α2,0 α3,0 α1,2 α1,3 α2,1 α3,1 α2,3 α3,2 δ1 δ2 δ3
Model 2 (growth)
The variables are excess return on the market index (i = 1), individual investor sentiments (i = 2), and institutional investor sentiments (i = 3). Note (*), (**), and (***) denote significance levels at the 10%, 5%, and 1%, respectively. Standard errors are in the parentheses. 237
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prices. Perhaps, although both individuals and institutions display significant sentiments, only institutions have enough market power to affect the volatilities. We investigate the possibility of asymmetric impact of the individual and institutional investor sentiments on stock market by examining the coefficients αi,j coupled with δj . Significant negative α1,2 and α13 coupled with a significant positive δ2 and δ3 imply that volatility spillover mechanism is asymmetric in both the cases. Specifically, there is greater effect of bullish than bearish investor sentiments on stock market volatility. This finding is consistent with the DHS model and other behavioral explanations (Brown and Cliff, 2006; Gervais and Odean, 2001; Wang, 2001; Hong et al., 2000) which suggest that the effect of sentiments on stock prices can be asymmetric. We also find significant parameters β2,1 and α2,1 which show that stock market returns and investor sentiments can act as a system and indicate a positive role of the stock market in the formation of individual investor sentiments. This finding suggests that individual investor sentiments show extrapolation bias to the extent that increased bullishness can be expected after a market rise and increased bearishness after a market fall (DeBondt, 1993), thereby making individuals “positive feedback traders”. This evidence is also consistent with the existence of bandwagon effect (Brown and Cliff, 2004) which states that stock returns predict future sentiments. However, in the case of institutional investor sentiments, we do not find the existence of such relationship suggesting that individuals, rather than institutions, are more likely to be positive feedback traders. Moreover, a significant α2,1 coupled with significant positive δ1 indicate the existence of asymmetric effect of stock market on individual investor sentiments. Innovations in stock market may have stronger effect on bullish sentiments during the period of growth than similar effects on the bearish sentiments during the period of decline. Lastly, we find significant α2,3 in case of DJIA while insignificant α3,2 in both the cases suggesting that that there is positive volatility spillover from the institutional to individual investor sentiments but not the other way round. This finding is consistent with the arguments of Nofsinger and Sias (1999) and Brown and Cliff (2004) which suggest that institutional investors have superior information and make up a disproportionately larger portion of the market relative to individuals. As such it is quite possible that individuals tend to follow institutional investor sentiments and not vice versa. In order to check the robustness of these results we make a distinction between the periods of growth and decline in the market. We split the sample into two periods, growth (1988–2001) and recession (2001–2004), and then re-estimate two additional models. Specifically, we estimate models 2 and 3 for the growth and recession period, respectively. The effect of individual and institutional investor sentiments on stock returns (β1,2 , β1,3 ) is significant in both the models. However, the magnitudes of these coefficients are much higher in the case of model 2. Similarly the response of market volatilities to investor sentiments (α1,2 and α1,3 ) is greater during the growth than recession period. In addition, we find significant α2,1 in model 2 and insignificant result in model 3. These findings suggest that individual investors have a greater (lesser) bandwagon effect and greater (lesser) positive feedback trading during a growth (decline) period. Similarly, the existence of asymmetry is higher in model 2 than 3. Overall, these findings indicate that the link between sentiments, market returns, and volatilities is stronger (weaker) during the phases of rally (decline) in the market. Table 4 reports the results of the residual-based diagnostic checks of multivariate EGARCH model for both DJIA and S&P500. The p values for Ljung-Box statistic for 12-order serial correlation of standardized residuals and the squared standardized residuals are insignificant in both cases. These results show that the multivariate EGARCH model can adequately describe the dynamic relationship between the three variables.
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Table 3 Effects of fundamentals on individual and institutional investor sentiments Variables
Sentt1
Sentt2
B10 Baa IIP HML INF Rm DIV SMB T30 T90 UMD USD C R2 SSR Akaike info criterion Schwarz criterion F-statistic Prob. (F-statistic)
−0.96 (0.88) −29.93*** (8.35) 1.30 (2.77) 1.44*** (0.53) −18.28*** (6.60) −6.75** (3.29) 8.32*** (3.31) 2.78*** (0.80) 7.47 (13.57) −13.11 36.71 0.00 (0.00) 0.00 (0.01) 0.29*** (0.07) 0.304 3.190 −0.839 −0.578 4.989 0.000
0.49 (0.71) −4.82 (8.27) −2.22 (2.20) 1.14*** (0.46) −8.35 (6.06) −3.60 (2.66) 4.50* (2.71) 1.99*** (0.66) −6.83 (11.51) −31.70 (31.64) 0.00 (0.00) 0.00 (0.01) 0.15** (0.07) 0.161 2.48 −1.090 −0.829 2.186 0.015
The variables are individual investor sentiments (Sentt1 ), institutional investor sentiments (Sentt2 ), economic growth (IIP), short-term interest rates (T30), economic risk premiums (T90), future economic variables (B10), business conditions (Baa), dividend yield (Div), inflation (INF), excess returns on market portfolio (Rm ), premium on portfolio of small stocks relative to large stocks (SMB), premium on portfolio of high book/market stocks relative to low book/market stocks (HML), momentum factors (UMD), and currency fluctuations (USD). Note (*), (**), and (***) denote significance levels at the 10%, 5%, and 1%, respectively. Standard errors are in the parentheses.
Since our primary focus is to analyze the relative effects of rational and irrational investor sentiments on stock market returns and volatility, we decompose the sentiment variables into rational and irrational components based on fitted and residual values of Eq. (2). Specifically, we estimate two separate ordinary least square (OLS) regressions based on Eq. (4). Table 3 reports the regression results. The individual investor sentiments (Sentt1 ) are significantly related to business conditions, inflation, dividend yield, excess returns on market, SMB, and HML. Similarly the institutional investor sentiments are significantly related to dividend yield, SMB, and HML. These results are consistent with the argument of Brown and Cliff (2006) that investor sentiments may contain a combination of both rational and irrational components and not necessarily only noise. We generate the fitted values (Sentˆtit ) and residuals (ξ it ) for each regression to compute the rational and irrational components of investor sentiments, respectively. To analyze the relative effects of rational and irrational investor sentiments on stock market returns and volatilities, as depicted in Eqs. (5)–(7), we estimate a set of multivariate EGARCH models for DJIA and S&P500. In addition to the returns on the two market indexes, we include the four new variables derived from Eq. (4) related to rational and irrational sentiments of individual and institutional investors. Table 4 reports the estimation results and diagnostics. In the mean equations there are significant positive effects of the rational individual (β1,2 ) and institutional (β1,4 ) investor sentiments on market returns. These results are consistent with our earlier findings that both individual and institutional investor sentiments significantly affect DJIA and S&P500 returns. Also, the effects of rational institutional investor sentiments are much higher than those of the rational individual investor sentiments for both the cases. Similarly the effects
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Table 4 Effects of rational and irrational sentiments of individual and institutional investors on DJIA & S&P500 excess return and conditional volatility
β1,0 β1,2 β1,3 β1,4 β1,5 β2,0 β2,1 β2,3 β2,4 β2,5 β3,0 β3,1 β3,2 β3,4 β3,5 β4,0 β4,1 β4,2 β4,3 β4,5 β5,0 β5,1 β5,2 β5,3 β5,4 α1,0 α2,0 α3,0 α4,0 α5,0 α1,2 α1,3 α1,4 α1,5 α2,1 α2,3 α2,4 α2,5 α3,1 α3,2 α3,4 α3,5 α4,1 α4,2 α4,3 α4,5 α5,1 α5,2 α5,3 α5,4
DJIA
S&P500
−0.0129 (0.0164) 0.0990** (0.0475) 0.0406 (0.0674) 0.1198*** (0.0300) −0.0311 (0.2200) 0.0967*** (0.0236) 0.6081 (16.7165) 0.0601 (1.9083) 0.0198 (6.1142) 0.0884 (2.9728) 0.0102 (0.5572) 0.0599* (0.0328) 0.0436 (5.6535) −0.0368 (11.9265) 0.0572 (8.8682) 0.0100*** (0.0027) 0.0489 (0.3829) 0.0505 (0.0921) 0.0500 (0.0491) 0.0499 (0.0934) 0.0100*** (0.0013) 0.0496 (0.2137) 0.0499 (0.0547) 0.0500** (0.2166) 0.0504 (0.1291) −0.2655 (37.9540) −4.8443 (30.4121) −1.3827 (17.0423) 0.0287 (8.6933) −0.0714 (5.3301) −0.1282 (2.3189) −0.1028* (0.0536) −0.0743 (4.4533) −0.1183* (0.0640) −6.7005 (28.4347) −0.0454 (21.7526) 0.1669 (12.1557) 0.0793 (4.7532) 1.1655** (0.5796) −0.0365 (1.4668) 0.0673 (6.9666) 0.0298 (4.5222) 0.1083 (1.2608) 0.0406 (3.6713) 0.0451 (7.0142) 0.0527 (1.0916) 0.0340 (0.0382) 0.0891 (1.6373) 0.0447 (3.4031) 0.0421 (1.3093)
0.0043 (0.0079) 0.0734** (0.0312) 0.0410* (0.0228) 0.0822*** (0.0239) 0.0509** (0.0251) 0.0711*** (0.0208) −0.0732 (0.1706) 0.0576 (0.0641) 0.3373 (0.2324) 0.0252 (0.0780) −0.0133 (0.0354) 0.1515** (0.0757) 0.1212 (0.3548) 0.0293 (0.5782) 0.0876 (0.1312) 0.0303 (0.0210) 0.1291 (0.2362) 0.1155 (0.1569) 0.0714 (0.0651) 0.0337 (0.0812) −0.0395 (0.0352) 0.8414 (0.6374) −0.5517 (0.5136) −0.1388 (0.1511) 1.0134 (0.7880) −2.7929* (1.5785) −1.1954 (1.1616) −3.1875** (1.5173) −4.6916** (2.2885) −5.6774*** (1.4504) −0.0620 (0.5628) −0.2570* (0.1475) 0.0680 (0.4954) −0.2024* (0.1220) 0.6115 (0.5715) 0.0269 (0.3158) −0.1167 (0.4919) 0.1742 (0.4583) 0.1273* (0.0713) −0.1763 (0.4964) 0.0891 (0.4613) −0.0014 (0.5071) −0.5393 (0.6255) 0.3585 (0.6186) 0.0464 (0.4399) 0.2215 (0.4600) 0.6273 (0.6381) −0.0690 (0.4169) 0.4588 (0.5384) 0.8593 (0.7413)
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Table 4 (Continued )
δ1 δ2 δ3 δ4 δ5
DJIA
S&P500
0.8949 (0.8625) 0.5272 (1.2377) 0.8603** (0.3690) 0.0998 (0.5386) 0.9975** (0.5459)
0.1036*** (0.0237) −0.0288 (0.0783) 0.1541*** (0.0468) 0.2685*** (0.0060) 0.5108* (0.2974)
Diagnostic checks: P-value statistics i=1 LB (12) LB2 (12)
0.253 0.145
i=2
i=3
i=4
i=5
i=1
i=2
i=3
i=4
i=5
0.250 0.125
0.158 0.158
0.148 0.124
0.212 0.198
0.413 0.325
0.223 0.256
0.254 0.221
0.189 0.279
0.256 0.298
The variables are excess return on the market index (i = 1), rational individual investor sentiments (i = 2), irrational individual investor sentiments (i = 3), rational institutional investor sentiments (i = 4), and irrational institutional investor sentiments (i = 5). Note (*), (**), and (***) denote significance levels at the 10%, 5%, and 1%, respectively. Standard errors are in the parentheses.
of irrational components of investor sentiments for both individuals (β1,3 ) and institutions (β1,5 ) in case of S&P500 are positive and significant. However, the effect of irrational sentiments is less than those of rational sentiments for both individual and institutional investors. These results indicate that the effect of investor sentiments on stock market returns is mainly attributed to the fundamental trading and less to the noise trading. In the variance equations, there are insignificant effects of the rational individual and institutional investor sentiments. Unlike the effects on the mean of stock market returns, the coefficients α12 and α14 are insignificant suggesting that rational sentiments does not cause a great deal of variability in stock prices. On the other hand, there are significant negative effects of irrational investor sentiments (α13 and α15 ) on stock market volatilities. The negative effect of irrational sentiments on volatility is consistent with the predictions of DSSW (1990) and other noise trader models that the effect of noise trading on expected returns is through its impact on the market’s formation of risk. Lastly, we find there are significant coefficients β3,1 and α3,1 which indicate that there are significant positive effects of stock returns and volatility in the formation of irrational sentiments of individual investors. These significant responses of irrational sentiments to stock market could explain the existence of positive feedback trading by individual investors. Conversely, there are insignificant effects of stock market returns and volatility (β5,1 and α5,1 ) in the case of rational investor sentiments. Insignificant results for rational and irrational institutional investor sentiments confirm the previous finding that institutional investors are less likely to be positive feedback traders. A significant δ1 coupled with positive α3,1 suggest greater effect of stock market innovations on bullish irrational sentiments during the period of growth than similar effects on bearish irrational sentiments during the period of decline. The P values for Ljung-Box statistic for 12-order serial correlation of standardized residuals and the squared standardized residuals show no evidence of first or second moment time dependencies in the standardized residuals. These diagnostic tests verify that the five variable multivariate EGARCH model are correctly specified. 5. Conclusion This study investigates the relative effects of fundamental and noise trading on the formation of conditional volatility of stock returns as suggested by DSSW (1990). We estimate a set of
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multivariate EGARCH model for DJIA and S&P500 returns. The first model is consistent with previous findings in that there are significant positive (negative) effects of investor sentiments on stock market returns (volatilities) for both individuals and institutions. We find these relationships to be asymmetric since there is a greater effect of bullish sentiments than bearish sentiments. The effect of the stock market on the formation of individual investor sentiments (institutional investor sentiments) is significant (insignificant). These results suggest that individuals are more likely to be positive feedback traders. We also find that individual investor sentiments react to institutional investor sentiments but not vice versa. Unlike previous studies which conjecture investor sentiments as fully irrational, we find that the individual and institutional investor sentiments are driven by both rational and irrational factors. The individual investor sentiments are significantly related to business conditions, inflation, dividend yield, excess returns on market, SMB, and HML. Similarly the institutional investor sentiments are significantly related to dividend yield, SMB, and HML. In the second model, we find that rational sentiments have greater positive effects on stock returns than the irrational sentiments for both individuals and institutions. In the case of volatility, we find significant negative effects of only the irrational component of sentiments. Consistent with behavioral theories, we find greater effects of irrational bullish sentiments than irrational bearish sentiments on the stock market for both individuals and institutions. However, in the case of rational sentiments, we do not find the existence of such asymmetric effects. Lastly, we find significant positive effects of stock returns and volatility in the formation of irrational sentiments of individual investors. These results may explain the positive feedback nature of individual investors. Evidence in favor of irrational sentiments is consistent with the view that investor error is a significant determinant of stock volatilities. The direct implication of these results is that conventional measures of temporal variation in risk omit an important source of risk: noise. Overall, the findings suggest that noise is a priced risk factor. We also find strong support for the role of economic fundamentals as determinants of stock market returns and volatility.
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