Does investor sentiment risk impact the returns and volatility of Islamic equities?
Last Modified: September 14, 2012
Abstract
In this paper, we estimate GARCH and VAR models to determine whether
investor sentiment impacts both the excess returns and volatility of various Dow Jones
Islamic equity indices. The results from GARCH estimations show that changes in
investor sentiment are positively correlated with the returns of Shariah-compliant
equities. In addition, we find the same result for the three firm-size portfolios (i.e., large-,
medium-, and small-cap). However, this relationship is stronger for harder to arbitrate
Shariah-compliant securities; that is, investor sentiment has a larger impact on small-cap
stocks. Estimations from the vector autoregressive model confirm the aforementioned
results. Our findings from GARCH estimations also suggest that bullish shifts in investor
sentiment in the current period are accompanied by lower conditional volatility in the
ensuing period. In general, these findings suggest that as noise traders create more risk
the market seems to reward them with higher expected returns.
Daniel Perez Liston
Prairie View A&M University
P.O. Box 519, MS 2310
Prairie View, TX 77446, USA
drperez@pvamu.edu
Sanzid Haq
Prairie View A&M University
P.O. Box 519, MS 2310
Prairie View, TX 77446, USA
sahaq@pvamu.edu
Daniel Huerta
University of Texas-Pan American
1201 West University Drive
Edinburg, TX 78539, USA
dhuerta@broncs.utpa.edu
JEL Codes: G02, G10, G11, G12
Keywords: Investor Sentiment, Volatility, GARCH, Islamic Equities
1.
Introduction
At the heart of modern financial theory lies the idea that markets are efficient and
that security prices act as precise signals for investors, so that they may allocate their
resources efficiently (Fama, 1970). Furthermore, the theory operates under the
assumption that investors’ demand for financial instruments is rational and driven only by
fundamental information. This means that, on average, security prices do not exhibit
significant pricing errors. However, this classical view of finance has come under
considerable attack as of late (Leroy and Porter, 1981; Shiller, 1981; De Bondt and
Thaler, 1985; Lee, Shleifer, and Thaler, 1991; Lee, Jiang, and Indro, 2002). In general,
the aforementioned studies suggest that market irregularities like the closed-end fund
puzzle and the underreaction and overreaction of stock prices, inter alia, are incompatible
with the concept of market efficiency. These results also suggest that a significant
number of investors seem to misperceive the true distribution of expected returns and as a
result their trading leads to security prices that are inconsistent with the concept of market
efficiency.
As a result of the consistency and regularity for which asset pricing anomalies are
observed in the literature, researchers have now begun to develop alternative models of
security prices that incorporate investor psychology. For example, Black (1986)
proposes a model where markets are inefficient. In his model, there are only two types of
traders; noise traders who trade on pseudo-signals and rational traders whose trading
decisions are based real signals. Because, in the model, noise traders are trading on
inaccurate information security prices can deviate from their true equilibrium value.
2
De
Long, Shleifer, Summers, and Waldman (1990), or DSSW as it is sometimes called,
extend Black’s model by building a theoretical model where stock prices maybe
influenced by noise trader risk. Their model attempts to explain various empirical
anomalies, and predicts that changes in the magnitude and direction of irrational noise
trader sentiment affect asset prices. Lee et al. (2002) suggest that noise traders usually
overreact to news. And depending on whether they are optimistic or pessimist, security
prices may be either above or below their equilibrium value. Noise trading may impact
security prices only if noise traders are continually making the same kind of mistakes.
For instance, large waves of investor pessimism will tend to generate underpricing due to
noise traders’ correlated trades. The literature finds such a systematic trading pattern
amongst noise traders, therefore suggesting that noise trading can influence equity prices
(Barber, Odean, and Zhu, 2009).
The impact of investor sentiment on the returns of equities has been empirically
tested. Many studies suggest that sentiment does influence asset prices (Lee, Shleifer,
and Thaler, 1991; Lee et al., 2002; Brown and Cliff, 2005; Baker and Wurgler, 2007; Ho
and Hung, 2009; Baker, Wurgler, and Yuan, 2009).1 These studies find a positive
contemporaneous relationship between investor sentiment and stock market returns.
Furthermore, the research also studies how stock market volatility is impacted by investor
sentiment (Brown, 1999; Lee et al., 2002). The results of these studies show that investor
sentiment and stock market volatility are correlated.
1
See Hirshleifer (2001) for a very detailed review of the literature.
3
The above-mentioned literature shows that investor sentiment plays a role in the
data generating process for equity returns. In spite of these findings, the literature on
Shariah-compliant securities has yet to examine if investor sentiment significantly
impacts the returns and volatility of Islamic equities (Hussein and Omran, 2005; Yusof
and Majid, 2007; Girard and Hassan, 2008; Kok et al., 2009; Perez-Liston and Soydemir,
2010; Alam and Rajjaque, 2010; Hayat and Kraeussl, 2011; Ferruz et al., 2012). To the
best of our knowledge this is the first article to examine the link between investor
sentiment and Shariah-compliant equities.
This study contributes to the literature in the following distinct ways. First, we
examine the impact of investor sentiment on Islamic equity excess returns. Second, we
study how investor sentiment might influence the conditional volatility of these
securities. Specifically, this study examines whether sentiment has an asymmetric impact
on the formation of conditional volatility. Third, in order to assess whether the impact of
investor sentiment varies across different size portfolios, we will examine these relations
for three portfolios formed on market capitalization. Fourth, because investor sentiment
and Shariah-compliant securities might behave as a system we examine the dynamic link
between these variables in a vector autoregressive setting. Lastly, more awareness is
drawn to one of the fastest growing equity classes, Islamic equities.
The results from GARCH estimations indicate that a positive change in investor
sentiment has a positive impact on the returns of Shariah-compliant equities. Similar
results hold for three firm-size portfolios (i.e., large-, medium-, and small-cap). In
particular, the results show that harder to arbitrate Shariah-compliant securities are more
4
susceptible to waves of investor sentiment; that is, investor sentiment has a larger impact
on small-cap stocks. Results also suggest that bullish shifts in sentiment are accompanied
by lower conditional volatility in the ensuing period. Furthermore, we find that this effect
is larger for small-cap stocks. On the other hand, bearish shifts in sentiment do not have a
significant impact on the conditional volatility. Finally, VAR model estimations suggest
that investor sentiment does influence the return generating process of Shariah-compliant
securities.
The remainder of this paper is organized as follows. Section 2 describes the
literature; Section 3 the data employed in the estimations; Section 4 describes the
econometric methodology; Section 5 describes the results; and Section 6 concludes.
2. Literature Review
A growing body of literature examines the risk-return characteristics of faith-based
and Shariah-compliant securities (Hussein and Omran, 2005; Yusof and Majid, 2007;
Girard and Hassan, 2008; Kok et al., 2009; Perez-Liston and Soydemir, 2010; Alam and
Rajjaque, 2010; Hayat and Kraeussl, 2011; Ferruz et al., 2012). On the one hand, some of
these studies find that Sharia investments exhibit superior risk-adjusted returns. For
instance, Hussein and Omran (2005) examine the returns of various Dow Jones Islamic
indexes and find that these provide abnormal returns over the entire sample and for bull
market periods. However, they also find that these indexes underperform under bear
market conditions. Alam and Rajjaque (2010) study the performance of Shariah-
5
compliant equities in the Europe markets for the Great Recession and find that they
outperform the market portfolio during this recent downturn.
On the other hand, some studies find that Shariah-compliant securities underperform
(Hayat and Kraeussl, 2011; Ferruz et al., 2012). For example, Hayat and Kraeussl (2011)
examine a sample of 145 Islamic equity funds (IFEs) and find that the returns of these
funds have underperformed both Islamic and secular equity benchmarks. In addition,
they find that IEF managers do a poor job in timing the market and as a result returns
suffer. Ferruz et al. (2012) examine the managerial abilities of religious mutual funds
managers and find that religious funds underperform relative to conventional funds.
Furthermore, they attribute this underperformance to the poor stock-picking (e.g., “Sin”
securities are excluded for most religious funds) and market timing of these managers.
The empirical evidence suggests that Shariah-compliant securities do not add
significant cost to investors (Guyot, 2011). For example, Guyot (2011) examined the
market quality and price dynamics of Islamic indexes. His findings suggest that Islamic
indexes do not impose additional liquidity or efficiency costs. But rather, these types of
indexes may increase diversification for international investors. Still, some studies find
no significant difference between secular and Islamic based investments. Girard and
Hassan (2008) examine Islamic versus non-Islamic indexes from 1999 to 2006 and find
no statistical difference in financial performance. Hakim and Rashidian (2004) find that
there is no loss, in terms of diversification, for the Dow Jones Islamic market index.
A small number of these studies have examined the volatility of these securities.
Yusof and Majid (2007) find that the volatility of the Malaysian Islamic stock market
6
index does not respond to interest rate volatility. Using co-integrations analysis, Hakim
and Rashidian (2004) find that the three-month interest rate is unrelated to the DJIMI. AlZoubi and Maghyereh (2007) find that the Dow Jones Islamic Market index outperforms,
in terms of risk, the Dow Jones World index.
Despite these findings, the aforementioned literature on Shariah-compliant
securities has yet to examine if investor sentiment significantly impacts the returns and
volatility of Islamic equities. To the best of our knowledge this will be the first article to
examine the link between investor sentiment and Islamic equities.
3. Data and Descriptive Statistics
The empirical analysis is conducted using weekly data retrieved from DataStream and
Ken French’s website.2 The sample spans from 1/12/1996 to 5/25/2012, for a total of 855
weekly observations.3 The variables used in the investigation are the: 1-month Treasury
bill from Ibbotson and Associates to proxy for the risk-free rate (Rft); return (in percent)
on the US Dow Jones Islamic Market index (Rt,SMKT); return on the US Dow Jones
Islamic large-cap index (Rt,SLG); US Dow Jones Islamic medium-cap index (Rt,SMD); US
Dow Jones Islamic small-cap index (Rt,SSM); first-difference in investor sentiment
(∆𝑆𝐸𝑁𝑇𝑡 = 𝑆𝐸𝑁𝑇𝑡 − 𝑆𝐸𝑁𝑇𝑡−1), proxied by the Investors Intelligence survey (II), where
𝑆𝐸𝑁𝑇𝑡 is calculated as the bull-bear spread. Positive changes in the investor sentiment
measure indicate bullishness by survey participants, whereas negative changes indicate
2
We would like to thank Ken French for making the data available on their website.
The sample begins in 1996, since data for the Shariah equities is first reported in DataStream as of
January of that year.
3
7
bearishness. One observation is lost when estimating the returns and the first-differences;
as a result the final sample consists of 854 weekly observations.
In addition, we compare the Sharia results to the various Dow Jones indexes: US
Dow Jones Market index (Rt,MKT); US Dow Jones large-cap index (Rt,LG); US Dow Jones
medium-cap index (Rt,MD); and US Dow Jones small-cap index (Rt,SM).
Table I presents the descriptive statistics for all the variables included in the study.
The average weekly returns during the sample for the US Dow Jones Islamic Market
index, US Dow Jones Islamic large-cap index, US Dow Jones Islamic medium-cap index,
and US Dow Jones Islamic small-cap index are 0.16 percent (8.32 annualized), 0.14
percent (7.28 annualized), 0.24 percent (12.48 annualized), 0.28 percent (14.56
annualized), respectively. Furthermore, the table also shows that risk (as measured by
std. dev.) was inversely related to firm size; the returns for smaller firms exhibited higher
volatility. The table also shows that there are considerable autocorrelations at the first (0.083), second (0.061), third (-0.038), and fourth (-0.063) lags for the US Dow Jones
Islamic Market index.4 This is consistent with Lo and MacKinlay’s (1988) result that
stock returns do not follow a random walk. It is also interesting to note that the
autocorrelations for investor sentiment are considerably higher than those of the Shariah
indexes, which indicates that investor sentiment exhibits a high degree of persistence.
Table II shows the correlation matrix for all the variables included in the study. The
estimated correlation coefficient (0.30) for investor sentiment and the returns on the
4
Correlograms are omitted for brevity, but are available upon request.
8
Shariah market portfolio return is positive and statistically significant at the 1 percent
level. Furthermore, the as firm size increases the correlation between investor sentiment
and shariah returns increases. For example, the correlation between the large portfolio
and institutional investor sentiment is 0.294, whereas the correlation between the small
portfolio and sentiment is 0.308.
4. Methodology
GARCH
This study examines the effect of sentiment on the returns and conditional volatility
of Islamic equities by estimating various GARCH models. Following Lee et al. (2002),
for each of the Islamic equity indexes (i.e., market, large-, medium-, and small-cap) we
estimate an augmented generalized autoregressive conditional heterokedasticity-in-mean
model (GARCH-M) for which the mean equation is of the following form5:
Rt ,i  Rf t   0  1 Jant   2Oct t   3 SENTt   4 ht   t ,
𝜀𝑡 ~ 𝑁(0, ℎ𝑡 ),
(1)
where Rt,i are the monthly returns for the ith portfolio, Rft is the risk-free rate, and ∆SENTt
is the change investor sentiment. In addition, Jant and Octt are dummy variables that take
the value of one in their respective months and zero otherwise. Furthermore, we assume
that the conditional variance evolves over time as follows:
5
Bollerslev et al. (1992) suggest that the GARCH (1, 1) is suitable for most econometric applications.
9
ht ,i  0  1 t21   2 t21I t 1  3ht 1   4 Rf t 1  5 (SENTt 1 ) 2 Dt 1  6 (SENTt 1 ) 2 (1  Dt 1 ),
(2)
where ht,i is the conditional variance and εt-1 the lagged error term. To capture the
asymmetric impact of sentiment on conditional volatility we set the dummy variable Dt-1
equal to zero if ΔSENTt-1 ≤ 0, and equal to one if ΔSENTt-1 > 0. Therefore, the coefficient
β5 captures the effect of bullish shifts in sentiment on return volatility and β6 captures
bearish shifts in sentiment. Additionally, the model accounts for the leverage effect by
setting the dummy variable It-1 equal to zero if εt-1 ≤ 0, and equal to one if εt-1 > 0
(Glosten, Jagannathan, and Runkle, 1993). Taken together, equations (1) and (2) form our
benchmark augmented GARCH-M model.
Empirical evidence suggests that the impact of sentiment on stock returns may be
larger in hard-to-arbitrage stocks (Baker and Wurgler, 2006), like small stocks.
Therefore, to examine the differential impact of investor sentiment on firm size portfolios
we estimate the GARCH-M models for the Dow Jones large-cap index, Dow Jones
medium-cap index, and Dow Jones small-cap index, in addition to the market portfolio.
In addition, we compare the GARCH results for the Islamic indexes to those of
the secular Dow Jones indexes (i.e., market, large-, medium-, and small-cap).
VAR
We estimate Sims’ (1980) vector autoregressive model (VAR) to assess the
dynamic relationships amongst Dow Jones Islamic returns and both types of investor
sentiment. The rationale for using the VAR model is that it will permit one to examine
10
the possible impact that innovations (shocks) from individual and institutional investor
sentiments might have on pure sin. Furthermore, there is evidence which suggests that
investor sentiment and Islamic returns might behave as a dynamic system (Brown and
Cliff, 2004). For comparison purposes, we also use the VAR model to examine the
impact of sentiments on the regural Dow Jones index. A mathematical representation of
an unrestricted VAR is as follows:
yt = A0 + A1yt -1 + …+ Apyt - p + et ,
(4)
where yt is a k vector of endogenous variables, A1 to Ap are matrices of coefficients to be
estimated and A0 is a vector of constants. In addition, et is a vector of innovations. The
appropriate lag length in the VAR is determined using Akaike’s information criterion
(AIC). The lags in the VAR model help capture the dynamic feedback amongst the
variables.
The generalized impulse response function is the main tool used for interpreting
the impact of sentiment shocks on the returns of the Islamic Dow Jones portfolios. The
benefit of using generalized impulse responses is that the ordering of the variables in the
VAR does not influence the impulse responses. For a detailed discussion of generalized
impulse response functions, see Pesaran and Shin (1998).
5. Results
GARCH Models: Institutional Investor Sentiment
11
Table ? reports the results for estimating the Lee et al. (2002) model using
institutional investor sentiment for the various Dow Jones Islamic indexes; market
portfolio, large-cap, medium-cap, and small-cap. The second column of the table shows
the coefficient estimates for the Islamic market portfolio. In the mean equation, the
coefficient for investor sentiment, 0.195, is positive and significant at the 1 percent level.
This suggests that as institutional investors become more optimistic returns for Islamic
equities, on average, tend to increase. This result is consistent with studies that have
examined the effect of investor sentiment on the market portfolio of secular equities (Lee,
Shleifer, and Thaler, 1991; Lee et al., 2002; Brown and Cliff, 2005; Baker and Wurgler,
2007; Ho and Hung, 2009; Baker, Wurgler, and Yuan, 2009). Furthermore, the GARCHin-mean term (0.069) is positive and statistically significant, indicating that volatility is
priced for the market portfolio. None of the coefficients for the seasonal dummy
variables (i.e., January and October) are significant, suggesting that the well-known
January effect and the October effect are not present in the data. In the variance equation,
the coefficient for positive changes in sentiment (-0.034) is statistically significant at the
1 percent level. This finding suggests that increased optimism by survey participants in
the current period, on average, leads to downward revisions in volatility for the following
period. On the other hand, the coefficient for negative changes in sentiment (-0.014) is
insignificant. The coefficient estimate (-17.249) for the risk-free rate is negative and
statistically significant; which is somewhat surprising, we would expect that the risk-free
rate is positively correlated with volatility. The insignificance of the leverage effect
12
coefficient (0.148) suggests that positive and negative innovations have the same impact
on conditional volatility.
To investigate if size-differential effects are present we estimate the GARCH
models for the large-, medium-, and small-cap Islamic indexes. For all three portfolios
the investor sentiment coefficient in the mean equation is both positive and significant.
Furthermore, we find that as firm size decreases, the role of investor sentiment becomes
more important. This finding is consistent with the prior literature, which suggests that
investor sentiment might play a larger role for hard-to-arbitrage stocks (Baker and
Wurgler, 2006). In the conditional variance equation, we find that for all size portfolios
positive changes in sentiment in the current period lead to downward revisions in
volatility for the following period; for example, the estimated coefficient on the large-cap
portfolio is -0.012. The results indicate that only the volatility of the large-cap portfolio
responds to bearish shifts in sentiment. Furthermore, we find that the risk-free rate is
significant for most size portfolios.
GARCH Models: Individual Investor Sentiment
Table ? reports the results for estimating the Lee et al. (2002) model using
individual investor sentiment for the four Dow Jones Islamic indexes. In Table ?, Column
???, the coefficient estimates for the Islamic market portfolio are shown. The coefficient
for investor sentiment, 0.013, in the mean equation is positive and significant at the 5
percent level. Although, this coefficient is smaller than the one for institutional investor
sentiment (0.195), it suggests that individual investor sentiment is positively correlated
with Islamic equities. Neither the GARCH-in-mean term, nor the seasonal dummy
13
variable coefficients (i.e., January and October) are significant. In the variance equation,
the coefficient for only positive changes in sentiment (-0.0009) is significant at the 5
percent level, however, the coefficient for negative changes in sentiment (0.001) is not.
The coefficient for the leverage effect (0.223) is statistically significant, indicating that
negative innovations have an asymmetric impact the formation of conditional volatility.
To investigate if size-differential effects are present using the individual investor
sentiment variable we ran the GARCH models for the large-, medium-, and small-cap
portfolios. For all three portfolios, the investor sentiment coefficients in the mean
equations are positive and significant. However, we find that as firm size increases the
impact of investor sentiment becomes less important. Furthermore, we find that volatility
is priced only for the medium-cap portfolio. In the conditional variance equation, for
three size portfolios, we find that positive changes in sentiment in the current period lead
to downward revisions in volatility for the following period. For example, the estimated
coefficient on the large-cap portfolio is -0.001. For bearish shifts in sentiment, none of
the coefficients are significant.
VAR Model: Shariah
Before proceeding with VAR estimations, we follow Brown and Cliff (2004) and
orthogonalize the Dow Jones Islamic small-cap portfolio; that is, we regress the smallcap portfolio on the large-cap portfolio and use the resulting residuals in the analysis.
14
This is done so that we can ensure that are results are driven by the “small” component of
returns.6 Furthermore, we also do the same for the secular Dow Jones index.
Figure ? shows the generalized impulse response functions for the large-cap and
small-cap Dow Jones Islamic indexes. The upper-left-hand panel of Figure ? illustrates
that a shock to individual investor sentiment, at impact, has a positive and significant
effect the returns of the large portfolio. And after 2 weeks, the returns are positive but
insignificant. The lower-left-hand panel of the figure shows that individual investor
sentiment, at impact, has a positive but insignificant effect on the small-cap portfolio. In
the upper-right-hand panel of Figure ?, the Monte Carlo constructed confidence bands
indicate that the returns of the large-cap portfolio react positively to institutional investor
sentiment shocks. After impact, the returns are monotonically decreasing and become
negative and significant after five weeks; indicating a reversal. In the lower-right-hand
panel of Figure ?, institutional investor sentiment has a positive and significant effect on
the returns of the small-cap portfolio.
VAR Model: Secular Dow Jones
Does investor sentiment have a similar impact on the secular Dow Jones
portfolios? To answer this question, run the VAR models using the secular Dow Jones
portfolios. Figure ? shows the generalized impulse response functions for the large and
small-cap Dow Jones portfolios. The upper-left hand panel of Figure ? shows that
individual sentiment has a large positive and significant impact on the returns of the
6
See Brown and Cliff (2004) for more information.
15
large-cap portfolio. However, after the first week the impact becomes insignificant. The
lower-left hand panel of Figure ? shows that individual investor sentiment does not have
an impact on the small-cap portfolio. In the upper-right hand panel of the figure, a shock
to institutional investor sentiment has a significant impact on the returns of the large-cap
portfolio. In the lower-right-hand panel, institutional sentiment has a significant and
positive effect on the small-cap portfolio. Interestingly after five weeks there is a renewed
impact on small portfolio returns. Comparing Figures ? and ?, it is important to note
that…
6. Conclusion
The extant literature on behavioral finance has focused mostly on how investor
sentiment impacts secular portfolio returns (Lee, Shleifer, and Thaler, 1991; Lee et al.,
2002; Brown and Cliff, 2005; Baker and Wurgler, 2007; Ho and Hung, 2009; Baker,
Wurgler, and Yuan, 2009), while completely ignoring the relation between investor
sentiment and Shariah-compliant securities. Therefore, almost nothing is known on how
waves of investor sentiment might influence the return and volatility generating processes
of Shariah-compliant securities in the U. S. This paper is an attempt to bridge this gap.
This article contributes to the literature by estimating GARCH and VAR models to assess
the role of investor sentiment on the excess return and conditional volatility of the
Shariah-compliant equities.
The results from GARCH estimations show that changes in investor sentiment
positively influence the returns of Shariah-compliant equities. These results are in
16
agreement with the findings for secular stock returns, where investor sentiment is
observed to have a positive impact on stock returns (Lee, Shleifer, and Thaler, 1991; Lee
et al., 2002; Brown and Cliff, 2005; Baker and Wurgler, 2007; Ho and Hung, 2009;
Baker, Wurgler, and Yuan, 2009). In addition, we confirm this relation for three firm-size
portfolios (i.e., large-, medium-, and small-cap). Consistent with prior studies of secular
portfolios, the results show that harder to arbitrate Shariah-compliant securities are more
susceptible to waves of investor sentiment; that is, investor sentiment has a larger impact
on small-cap stocks. In general, these findings suggest that as noise traders create more
risk the market seems to reward them with higher expected returns.
In addition the GARCH results suggest that bullish shifts in sentiment are
accompanied by lower conditional volatility in the ensuing period. Furthermore, we find
that this effect is larger for small-cap stocks. On the other hand, bearish shifts in
sentiment do not have a significant impact on the conditional volatility.
There is evidence which suggests that investor sentiment and Islamic returns
might behave as a dynamic system (Brown and Cliff, 2004). Therefore, we estimate a
VAR model. The results of the VAR model suggest that investor sentiment does
influence the return generating process of Shariah-compliant securities.
The results in this study largely suggest that the traditional view of finance (i.e.,
rational expectations) cannot complete account for the variation of Shariah-compliant
equity returns and volatility. Accordingly, to fully understand the returns and volatility of
Shariah-compliant equities one needs to account for the role of investor sentiment.
17
18
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21
Table 1. Descriptive statistics.
Std.
Mean
Dev.
Max.
Min.
ρ1
ρ2
ρ3
ρ4
Rt,SMKT
0.163
2.740
10.725 -17.623 -0.083
0.061
-0.038
-0.063
Rt,SLG
0.143
2.652
10.110 -17.958 -0.095
0.062
-0.044
-0.066
Rt,SMD
0.243
3.328
14.926 -17.580 -0.041
0.050
-0.011
-0.040
Rt,SSM
0.286
3.607
14.980 -19.303 -0.008
0.046
0.011
-0.029
0.135
2.671
12.858 -18.001 -0.068
0.056
-0.052
-0.045
Rt,MKT
0.128
2.681
12.332 -18.179 -0.073
0.036
-0.059
-0.049
Rt,LG
0.185
3.058
16.899 -18.531 -0.051
0.045
-0.043
-0.038
Rt,MD
0.185
3.277
17.295
-19.551
-0.039
0.044
-0.037
-0.035
Rt,SM
SENTIIt -0.003 4.728
18.100 -17.500 0.151
0.048
-0.013
-0.097
SENTAA
IIt
-0.042 15.410 50.750 -56.970 -0.337
-0.019
-0.050
-0.012
Rft
0.059
0.044
0.140
0.000
0.995
0.990
0.984
0.979
Notes: This table reports the descriptive statistics for the variables used in the
investigation. These are the: 1-month Treasury bill from Ibbotson and Associates to
proxy for the risk-free rate (Rft); return (in percent) on the US Dow Jones Islamic Market
index (Rt,SMKT); return on the US Dow Jones Islamic large-cap index (Rt,SLG); US Dow
Jones Islamic medium-cap index (Rt,SMD); US Dow Jones Islamic small-cap index
(Rt,SSM); institutional investor sentiment 𝑆𝐸𝑁𝑇𝐼𝐼𝑡 , proxied by the Investors Intelligence
survey (II); individual investor sentiment 𝑆𝐸𝑁𝑇𝐴𝐴𝐼𝐼𝑡 , proxied by the American
Association of Individual Investors survey. Also included in the study are the: return (in
percent) on the US Dow Jones Market index (Rt,MKT); return on the US Dow Jones largecap index (Rt,LG); US Dow Jones medium-cap index (Rt,MD); and the US Dow Jones
small-cap index (Rt,SM). The sampled period is from January 12, 1996 to July 15, 2012.
The empirical analysis is conducted using weekly data retrieved from DataStream and
Ken French’s website.
Table ?
GARCH-in-mean Model Estimations for Dow Jones Islamic Indexes
Rt,SMKT
Rt,SLG
Rt,SMD
Rt,SSM
ht
0.069**
0.039
0.070
0.043
Jan t
-0.038
0.133
0.044
0.264
Oct t
-0.414
0.029
-0.447
-0.668**
ΔSENTt
0.195***
0.169***
0.211***
0.235***
β0
4.971***
0.267***
7.898***
9.330***
2
ε t-1
0.120
0.053
0.113
0.104
2
ε t-1 It-1
0.148
0.228***
0.133
0.118
ht-1
0.502**
0.781***
0.491***
0.514***
R f, t
-17.24***
1.840*
-24.70***
-29.361***
2
(ΔSENTt-1) Dt-1
-0.034***
-0.012***
-0.049***
-0.056***
2
(ΔSENTt-1) (1-Dt-1)
-0.014
0.011**
-0.024
-0.026
Log-likelihood
-2006.98
-1893.99
-2168.52
-2251.91
Notes: Table ? reports the results from estimating the GARCH-in-mean models with
investor sentiment described in the text in equations (?) and (?). The estimation period is
from January 12, 1996 to July 15, 2012. The empirical analysis is conducted using
weekly data retrieved from DataStream and Ken French’s website. *, **, *** denotes
significance at the 10%, 5%, and 1% level, respectively. Jant and Octt are dummy
variables that take the value of one in their respective months and zero otherwise. The
variables used in the investigation are the: 1-month Treasury bill from Ibbotson and
Associates to proxy for the risk-free rate (Rft); return (in percent) on the US Dow Jones
Islamic Market index (Rt,SMKT); return on the US Dow Jones Islamic large-cap index
(Rt,SLG); US Dow Jones Islamic medium-cap index (Rt,SMD); US Dow Jones Islamic smallcap index (Rt,SSM); first-difference in investor sentiment (∆𝑆𝐸𝑁𝑇𝑡 = 𝑆𝐸𝑁𝑇𝑡 − 𝑆𝐸𝑁𝑇𝑡−1),
proxied by the Investors Intelligence survey (II), where 𝑆𝐸𝑁𝑇𝑡 is calculated as the bullbear spread.
23
Individual and Institutional Sentiment
Conditional volatility, excess return, and sentiment index
January 12, 1996 - July 15, 2013
Base model
Market
Sentaaii
Sentii
ht
0.063*
0.067*
Jan t
Oct t
ΔSENTt
-0.048
-0.025
0.000
-0.122
0.016***
0.169***
β0
0.352*
0.354***
ε2t-1
-0.000
0.044
ε2t-1 It-1
0.275***
0.255***
ht-1
R f, t
0.796***
0.144
0.770***
0.373
(ΔBCIt-1)2Dt-1
-0.000
-0.010***
(ΔBCIt-1) (1-Dt-1)
0.001
0.010*
Log-likelihood
-1924.61
-1874.52
2
24
Dow Jones Industrial Average
Conditional volatility, excess return, and sentiment index, January 12, 1996 - July 15,
2012
Base model
Rt,MKT
Rt,LG
Rt,MD
Rt,SM
ht
0.024
0.041
0.038
0.039
Jan t
Oct t
ΔSENTt
-0.013
-0.090
0.094
0.078
-0.129
-0.031
-0.038
-0.000
0.175***
0.158***
0.171***
0.202***
β0
4.951***
0.265***
7.026***
8.023***
ε2t-1
0.114**
0.010
0.100
0.085
ε2t-1 It-1
ht-1
R f, t
0.085
0.503***
-14.73***
0.201***
0.818***
2.442*
0.053
0.525***
-13.20**
0.045
0.525***
-13.04
(ΔBCIt-1)2Dt-1
-0.033***
-0.015***
-0.044***
-0.048***
(ΔBCIt-1)2(1-Dt-1)
0.005
0.019**
-0.013
-0.015
Log-likelihood
-1971.06
-1901.11
-2123.04
-2189.54
25
Table ?
VAR-Dow Jones returns and investor sentiment changes
Independent
Dependent
variable
Lag
variable
∆SENTAAII
∆SENTII
Rt,LG
Rt,SOB
∆SENTAAII
1
-0.556***
0.024**
-0.000
-0.002
2
-0.343***
0.030**
0.013
0.004
3
-0.291***
0.020
0.002
-0.003
4
-0.180***
0.011
-0.006
-0.011**
5
-0.150***
0.010
-0.013*
-0.007*
6
-0.108***
-0.002
-0.013*
-0.000
∆SENTII
1
0.672***
0.015
0.058***
-0.010
2
0.204*
-0.044
0.033
-0.002
3
0.085
-0.026
0.035
-0.003
4
-0.228**
-0.090**
-0.012
0.040***
5
-0.016
-0.037
0.002
-0.003
6
-0.203**
-0.071**
-0.001
-0.004
Rt,MKT
1
1.448***
0.440*** -0.112*** 0.057***
2
-0.279
0.162**
-0.023
0.031
3
-0.209
0.037
-0.113***
0.007
4
0.075
-0.053
-0.054
0.016
5
-0.006
0.017
0.070*
0.012
6
0.148
-0.066
0.090**
0.024
Rt,SOB
1
0.821***
0.137
-0.061
-0.041
2
-0.373
0.176
-0.051
0.053
3
-0.512
-0.103
-0.060
0.079**
4
-0.306
-0.006
-0.007
-0.037
5
-0.526*
0.094
0.051
-0.025
6
0.385
-0.023
-0.072
-0.086**
Constant
-0.242
-0.065
0.144
-0.015
Block Exogeneity
0.000***
0.000***
0.050*
0.006***
2
R
0.311
0.097
0.022
0.029
The variables included in the vector autoregressive model are the change in individual
investor sentiment (∆SENTAAII), the change in institutional sentiment (∆SENTII), the
returns on the large-cap portfolio (Rt,LG), and the returns on the small-cap portfolio
orthogonal to large stocks (Rt,SOB). We report the p-value for the Block Exogeneity
𝜒 2 (Wald) test. The null hypothesis for this test is that the coefficients on all lags of all
independent variables (other than the own lags of the endogenous variable) are jointly
zero. The sample consists of 854 weekly observations starting on January 12, 1996
through July 15, 2012. *, **, *** denotes significance at the 10%, 5%, and 1% level,
respectively.
26
S&P Weekly VAR-returns and filtered sentiment levels
Independent variable
Lag Dependent variable
∆SPDAAII
∆SPDAAII
1
0.394***
2
0.188***
3
0.030
4
0.085**
5
0.012
6
0.061*
∆SPDII
1
0.627***
2
-0.433***
3
-0.129
4
-0.312**
5
0.212
6
0.043
Rt,LG
1
1.544***
Rt,SOB
Constant
Block Exogeneity
R2
∆SPDII
0.023*
0.008
-0.008
-0.007
0.000
0.000
0.959***
-0.061
0.006
-0.069
0.045
0.022
0.469***
Rt,LG
0.001
0.015*
-0.008
-0.007
-0.004
0.007
0.053**
-0.025
0.000
-0.051*
0.014
0.003
-0.109***
Rt,SOB
-0.001
0.006
-0.007*
-0.007
0.003
0.008**
-0.012
0.007
-0.001
0.043***
-0.045***
0.003
0.057***
2
3
4
5
6
1
-0.090
-0.049
0.226
0.194
0.199
0.954***
0.224***
0.102
0.014
0.085
-0.035
0.146
-0.024
-0.114***
-0.059
0.071*
0.079**
-0.053
0.031
0.007
0.016
0.012
0.022
-0.041
2
3
4
5
6
-0.279
-0.415
-0.233
-0.331
0.457
1.935**
0***
0.572
0.180*
-0.068
0.027
0.145
0.012
1.514***
0***
0.893
-0.047
-0.064
-0.014
0.058
-0.071
0.221
0.110
0.018
0.051
0.078**
-0.037
-0.023
-0.087**
0.032
0.005***
0.030
The variables included in the vector autoregressive model are the change in individual
investor sentiment (∆SENTAAII), the change in institutional sentiment (∆SENTII), the
returns on the large-cap portfolio (Rt,LG), and the returns on the small-cap portfolio orthogonal
to large stocks (Rt,SOB). We report the p-value for the Block Exogeneity 𝜒 2 (Wald) test. The
null hypothesis for this test is that the coefficients on all lags of all independent variables
(other than the own lags of the endogenous variable) are jointly zero. The sample consists of
27
854 weekly observations starting on January 12, 1996 through July 15, 2012. *, **, ***
denotes significance at the 10%, 5%, and 1% level, respectively.
28
Weekly VAR-Shariah Levels and filtered sentiment
levels
Independent variable
Lag Dependent variable
∆SENTAAII
∆SENTAAII
∆SENTII
Rt,LG
Rt,SOB
Rt,LG
1
2
3
4
5
6
1
2
3
4
5
6
1
0.387***
0.189***
0.037
0.089**
0.015
0.053
0.563***
-0.416***
-0.069
-0.315**
0.238
0.014
1.658***
0.022*
0.010
-0.007
-0.004
-0.000
-0.001
0.940***
-0.050
0.024
-0.069
0.050
0.010
0.532***
-0.000
0.014*
-0.015*
-0.008
-0.002
0.010
0.046**
-0.045
0.001
-0.057*
0.018
0.023
-0.124***
-0.003
0.002
-0.007
-0.002
0.007
0.011**
-0.018
0.031
-0.009
0.019
-0.050**
0.022
0.106***
Rt,SOB
2
3
4
5
6
1
0.210
-0.059
0.131
0.229
0.192
1.164***
0.270***
0.107
-0.037
0.084
-0.004
0.150*
0.018
-0.064
-0.042
0.115***
0.126***
0.000
0.040
0.014
0.031
0.039
0.034
-0.017
2
3
4
5
6
0.011
-0.312
-0.137
-0.393*
0.175
1.721**
0***
0.581
0.137*
-0.014
-0.024
0.030
-0.008
1.414***
0***
0.896
-0.021
0.047
0.003
0.012
-0.050
0.383**
0.050*
0.036
0.007
0.066*
0.016
0.015
-0.001
-0.010
0.006***
0.021
∆SENTII
Constant
Block Exogeneity
R2
The variables included in the vector autoregressive model are the change in individual
investor sentiment (∆SENTAAII), the change in institutional sentiment (∆SENTII), the
returns on the large-cap portfolio (Rt,LG), and the returns on the small-cap portfolio orthogonal
to large stocks (Rt,SOB). We report the p-value for the Block Exogeneity 𝜒 2 (Wald) test. The
null hypothesis for this test is that the coefficients on all lags of all independent variables
(other than the own lags of the endogenous variable) are jointly zero. The sample consists of
854 weekly observations starting on January 12, 1996 through July 15, 2012. *, **, ***
denotes significance at the 10%, 5%, and 1% level, respectively.
29
Weekly VAR-Shariah returns and filtered sentiment levels
Independent variable
Lag Dependent variable
∆SENTAAII
∆SENTII
∆SENTAAII
Rt,LG
Rt,SOB
Rt,LG
1
2
3
4
5
6
1
2
3
4
5
6
1
-0.562***
-0.346***
-0.288***
-0.174***
-0.142***
-0.104***
0.599***
0.148
0.084
-0.236**
-0.001
-0.191*
1.608***
0.023*
0.030**
0.021
0.015
0.012
-0.001
-0.007
-0.055
-0.021
-0.087**
-0.030
-0.065*
0.518***
-0.000
0.014*
-0.002
-0.011
-0.017**
-0.014**
0.056***
0.012
0.014
-0.040*
-0.020
-0.005
-0.130***
-0.004
-0.003
-0.011*
-0.015**
-0.007
0.005
-0.018
0.013
0.005
0.025
-0.023
-0.022
0.106***
Rt,SOB
2
3
4
5
6
1
0.072
-0.174
0.043
0.099
0.178
1.018***
0.223***
0.055
-0.089
0.040
-0.020
0.136
0.009
-0.072*
-0.043
0.109***
0.131***
-0.010
0.041
0.017
0.031
0.044
0.043
-0.015
2
3
4
5
6
-0.147
-0.458*
-0.239
-0.563**
0.107
-0.343
0***
0.325
0.120
-0.048
-0.056
-0.013
-0.036
-0.095
0***
0.119
-0.033
0.038
0.000
0.001
-0.051
0.128
0.050*
0.038
0.016
0.071**
0.019
0.015
0.002
-0.039
0.006***
0.023
∆SENTII
Constant
Block Exogeneity
R2
The variables included in the vector autoregressive model are the change in individual investor
sentiment (∆SENTAAII), the change in institutional sentiment (∆SENTII), the returns on the
large-cap portfolio (Rt,LG), and the returns on the small-cap portfolio orthogonal to large stocks
(RSt,SOB). We report the p-value for the Block Exogeneity 𝜒 2 (Wald) test. The null hypothesis for
this test is that the coefficients on all lags of all independent variables (other than the own lags
of the endogenous variable) are jointly zero. The sample consists of 854 weekly observations
starting on January 12, 1996 through July 15, 2012. *, **, *** denotes significance at the 10%,
5%, and 1% level, respectively.
30
Covariance Analysis: Ordinary
Date: 08/29/12 Time: 09:41
Sample (adjusted): 1/19/1996 5/25/2012
Included observations: 854 after
adjustments
Correlation
Probability Rt,SMK
Rt,SLG
Rt,SMK
1.000000
-----
Rt, SMD
Rt,SSM
SENTIIt SENTAAIIt Rt
Rt,SLG
0.994743 1.000000
0.0000 -----
Rt, SMD
0.943063 0.905023 1.000000
0.0000 0.0000 -----
Rt,SSM
0.897811 0.853393 0.963862 1.000000
0.0000 0.0000 0.0000 -----
SENTIIt
0.301708 0.294634 0.294294 0.308443 1.000000
0.0000 0.0000 0.0000 0.0000 -----
Rft
SENTAAIIt 0.120329 0.117871 0.119017 0.125858 0.177228 1.000000
0.0004 0.0006 0.0005 0.0002 0.0000 ----Rt
0.971118 0.957853 0.942305 0.906226 0.323472 0.146229 1.000000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
-----
Rft
0.017416 0.021927 0.001633 0.009811 -0.005986 1.000000
0.017021
0.010124
0.6113 0.5222 0.9620 0.7746 0.6194 0.8613
0.7677 -----
31