Investor sentiment and stock market liquidity: Evidence from an emerging economy

Journal of Behavioral and Experimental Finance 23 (2019) 166–180

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Investor sentiment and stock market liquidity: Evidence from an emerging economy Jyoti Kumari Indian Institute of Management (IIM) Sambalpur, Jyoti Vihar, Burla, Sambalpur 768 019, Odisha, India

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Article history: Received 22 January 2019 Received in revised form 18 June 2019 Accepted 17 July 2019 Available online 25 July 2019 JEL classification: C2 C3 C5 G1 G4

a b s t r a c t I investigate the relationship between the stock market liquidity and investors sentiment. The significance of the liquidity in asset pricing is well documented, but little attention is paid in the empirical literature to the effect of investors sentiment on variation in the liquidity. I construct irrational aggregate sentiment index (ASI) measure the institutional investors sentiment. The empirical findings suggest that the stock market is highly liquid when sentiment is bullish and vice versa. Using the non-linear conditional volatility framework and non-linear Granger causality, I show the significant role of investors sentiment in predicting the stock market liquidity. The past psychological biases and herding of investors are associated with the volatility of liquidity through the direct and indirect channels. © 2019 Elsevier B.V. All rights reserved.

Keywords: Investors sentiment Stock market liquidity Irrational investors sentiment Volatility Non-linearity India

1. Introduction In this paper, I examine the relationship between aggregate stock market liquidity and investor sentiment in the non-linear conditional mean–variance framework. The extant literature focuses on how the liquidity affects the stock returns whereas a few studies examine the sources of the variations in the stock market liquidity (Chordia et al., 2001, Amihud, 2002). A couple of studies document the macroeconomic factors affecting the stock market liquidity and the intertemporal relationships between market liquidity, returns and volatility (e.g., Chowdhury et al., 2018). The recent evidence from the school of behavioral finance emphasizes the role of investor sentiment in the asset pricing (Baker and Wurgler, 2006; Baker et al., 2012), the behavior of returns and volatility. However, the literature has paid little attention to evaluate the relationship between investor sentiment and stock market liquidity. Intuitively hypothesize that investor sentiment can have direct and indirect effects on the stock market liquidity. In the case of direct effects, bullish investor sentiment affects the liquidity through noise traders (Black, 1986) and irrational market makers (Shiller, 2000). The earlier theoretical framework of De Long et al. E-mail address: [email protected]. https://doi.org/10.1016/j.jbef.2019.07.002 2214-6350/© 2019 Elsevier B.V. All rights reserved.

(1990a,b), Kyle (1985), and Lee et al. (1991) incorporate the significant role of noise traders in asset pricing. Such function, in turn, expected to affect the market liquidity. In the indirect effects, Baker and Stein (2004) propose a model in which sentiment is higher when a large number of irrational market makers exists in the markets. As these irrational market makers are assumed to underreact or overreact to the information contained in the order flows, the price impact caused by such order flows is lower, and hence liquidity increases. The higher sentiment reflects a higher level of overconfidence in the markets, and such overconfidence increases stock market liquidity (Odean, 1998). Despite such theoretical linkage between liquidity and sentiment, empirical evidence on the relationship is scarce particularly in emerging markets (EMs) (e.g., Ogunmuyiwa, 2010; Debata et al., 2017). The relationship between microstructure variables such as liquidity and behavioral factors such as sentiment offers intriguing insights into working of real-world financial markets. Against this backdrop, I examine the relationship between liquidity and sentiment and contribute to the nascent literature in many folds. First, the present study is first work on liquidity and sentiment in EMs. The work of Liu (2015) is the sole empirical study on the issue exclusively focusing on the US market. The work Liu (2015) ignored the time varying nature of liquidity and sentiment. Our study addresses this issue and thus departs

J. Kumari / Journal of Behavioral and Experimental Finance 23 (2019) 166–180

from previous work. Further, the findings on the free market benchmark such as the US are inapplicable to the EMs such as India with the equal force due to peculiar characteristics of the latter. The friction such as non-synchronous trading, lack of liquidity, the dominance of institutional traders, higher volatility, poor disclosure norms, lack of regulation, etc. characterizes the EMs. At the same time, these markets offer higher returns and better diversification opportunities. The issue also assumes significance because of financial liberalization, international portfolio diversification, the exponential increase in the market capitalization, and faster economic growth of the EMs. Therefore, the sample from India, the second faster-growing economy is an ideal candidate for the empirical investigation. Thus, this study also extends the literature on sentiment in EMs. Second, the present study develops an aggregate sentiment index (ASI) for India following the top-down approach of Baker and Wurgler (2007). Our sentiment index includes aggregate market sentiment indicators related to market performance, types of trading activity, derivative variables, and other sentiment proxies. Third, I examine the role of institutional investor sentiment in determining the stock market liquidity. Previous research focuses on the impact of investor sentiment on the stock market liquidity in the developed markets in which the retail investors dominate and noise trading due to them has a substantial effect on the market (Brown and Cliff, 2004). The extant studies have not addressed the question of how institutional investor sentiment is priced in the EMs. Theoretically, the institutional investors are informed and rational arbitrageurs, they trade on fundamentals. Nevertheless, institutional investors in EMs such as India often trade against market fundamentals and act irrationally with the optimism and herding attitude to gain extra risk premium from the markets. Therefore, such traders drive the prices against intrinsic values. Hence, the issue of how institutional investor sentiment affects liquidity assumes significance in the EMs such as India. Fourth, noise trading drives the prices away from the fundamentals and often leads to higher volatility. Such higher volatility due to sentiment in the market eventually threatens the stability of financial markets (Shleifer and Summers, 1990). The higher volatility because of noise traders increases the cost of trading for the market participants and thus adversely affect the market liquidity. Therefore, the institutional investor sentiment and stock market liquidity relationship poses important research questions and the nexus is significant from the perspective of market reforms and microstructure changes in India. Fifth, the study employs the set of non-linear GARCH class of models to find out the positive and negative effects of institutional investor sentiment on the stock market liquidity volatility. The non-linear GARCH models are comprehensive tools and provide intriguing insights to understand the time variation of liquidity. I introduce sentiment in the mean–variance framework to capture the stylized facts such as volatility persistence, clustering and asymmetry characteristics for the stock market liquidity. I probe how time varying liquidity volatility is dependent on the time varying sentiment. The evidence from the previous work on the issue failed to capture the time variation and non-linearity. The remainder of the paper organized as follows. In Section 2, I present the theoretical framework and the empirical literature and describe the methodology in Section 3. In Section 4, I explain the data and the construction of the liquidity and investor sentiment variables whereas I discuss the empirical results in Section 5. I conclude the paper in the last section.

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2. Theoretical framework and empirical literature The modern theory of finance postulates that asset prices tend to move closer to the fundamental values and self-correcting mechanism corrects any disruptions in the prices, and thus markets are efficient in the long-run. This proposition assumes market participants as rational risk-averse arbitragers and believes in the subjective expected utility maximization. Hence, the fundamental factors alone influence asset prices, cross-sectional returns, and liquidity in the financial markets. Of late, the assumption of rationality has further come under scathing criticism after its failure to explain several empirical departures of efficient markets convincingly. Behavioral finance, the new approach to finance emerged as a response to the limitations of the neoclassical framework. Kahneman and Tversky (1974) in their prospect theory explain that judgments under uncertainty are derived by the human heuristics and biases which represents the preferences of investors.1 Future beliefs of the agents are reflected through the judgments based on the overconfidence (Fischhoff et al., 1997), optimism and wishful thinking (Weinstein, 1980; Buehler et al., 1994), representativeness and anchoring (Kahneman and Tversky, 1974), and conservatism (Edwards, 1968). In light of such influence of behavioral aspects, the previous work on liquidity, based purely on the neoclassical framework is incomplete. Hence, understanding whether the behavioral variable such as sentiment affects the liquidity is essential. The theoretical literature from microstructure and behavioral finance suggest a relationship between market liquidity and investor sentiment. The theoretical framework intuitively highlights that investor sentiment affects market liquidity through the participants in the financial markets. It is important to understand how market participants can have an indirect effect on liquidity as sentiment affects the market liquidity via market participants. Kyle (1985) was first to present a theoretical model to elucidate the relationship between investor sentiment and liquidity through market participants’ channel. Kyle’s (1985) model include essentially three types of market participants— insider traders, noise traders, and, rational market makers. First, the private information mainly derives the trading strategies and investment patterns of insider trading; order flow of such trading is based on private information and thus the price impact in the markets is due to such insider trading. The price impact imperatively affects market liquidity. Second, behavioral theories posit certain plausible features of assets interpreted as deviations from fundamental values owing to noise traders (Barberis and Thaler, 2003). The DSSW noise-traders approach of De Long et al. (1990a,b) and Shleifer and Vishny (1997) show how noise traders are the long-term investor in the markets and these traders act on non-fundamental information in the markets and affect the asset prices and liquidity of the markets in a systematic way (Brown, 1999). The noise traders trade on non-fundamental information which is nothing but irrational trading activity. Such trading leads to higher sentiment and drives the prices away from intrinsic values. Such deviation, in turn, increases the market liquidity (Kyle, 1985; De Long et al., 1990a,b). Kyle (1985) demonstrates that greater noise trading leads to higher market liquidity. Because the higher number of noise traders in the market makes the market makers believe that the proportions of insider trading in the order flow are lower. Hence, the price impact of such order flow is lower owing to smaller price adjustment by the market makers; and this lower price impact increases the liquidity. 1 For the detailed discussion, see, Kahneman et al. (1982), Camerer (1995) and Kahneman and Tversky (2000).

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Third, the rational market makers who receive the order-flows from the insiders and the noise traders set the efficient price at which they trade. Since the market makers do not distinguish between the orders of noise traders and the insider traders, they always adopt the linear pricing rule for the trading strategy. Therefore, the theoretical framework of Kyle (1985) asserts the impact of the behavior of these three participants—insider traders, noise traders and market makers on the market liquidity indirectly. In these lines, Baker and Stein (2004) propose a unified theoretical framework to show the association between investor sentiment and market liquidity. The unified theoretical model of Baker and Stein (2004) illustrate a direct relationship between liquidity and sentiment of irrational investors. Investor sentiment increases the stock market liquidity when higher investor sentiment creates more irrational noise traders. According to Baker and Stein (2004), rational market makers are assumed to infer the insider information correctly, and thus their order flows are efficient. But the irrational traders are driven by the psychological biases, herding, and overconfidence and overreact or underreact to such information. Therefore, in the presence of short sale constraints, a liquid market reflects the dominance of irrational investor who tends to underreact to the information contained in either order flow or equity stocks. Hence, higher liquidity in the market is a sign of positive sentiment in the market dominated by irrational investors. In this light, the role of investor sentiment in determining stock market liquidity assumes significance. Nonetheless, an empirical inquiry into the issue is scant. Liu (2015) employs the Granger causality test and the linear regression to analyze the interrelationship between liquidity and investor sentiment empirically. Their findings support the theoretical predictions of Baker and Stein (2004) that investor sentiment in the US market increases market liquidity. But they applied static method whereas the relationship between these two variables is expected to be dynamic. The evidence on the ideal free market such as the US hardly offers insights into the working of EMs. A couple of studies attempt to understand the issue of liquidity and investor sentiment in EMs but differ in their perspectives. Ogunmuyiwa (2010) attempts to empirically analyze the interlinkage between investor sentiment, liquidity and economic growth in Nigeria and reveal that investor sentiment and stock market liquidity are critical ratios for stock market growth and development. Similarly, Lin (2015) employing the VAR systems conclude that when the investors are pessimistic in the markets, liquidity can be fragile; a small mutual fund outflow can lead to a large decline in market liquidity of the assets held by the funds and vice versa. Further, Debata et al. (2017) empirically examined the investor sentiment and stock market liquidity in select EMs. The study shows that sentiment is one of the significant factors for the variation in stock market liquidity in the EMs. Moreover, the study claims the contagious sentiment effect in these markets. Besides, a few empirical studies focus on investor sentiment and the stock price volatility in EMs (Kumari and Mahakud, 2016; Labidi and Yaakoubi, 2016; Rupande et al., 2019). The review of the literature shows that a handful of prior studies theoretically and empirically examined investor sentiment, asset price volatility, and liquidity. Nevertheless, liquidity and sentiment relationship is not the central question in these studies. A couple of them employed survey method which is not relevant to the EMs which are dominated by institutional traders. The hitherto studies also used the narrow method of sentiment. Further, there is a paucity of the studies focusing on the time varying investor sentiment, particularly in the nonlinear framework. Thus, the present study bridges these gaps in the literature especially by providing evidence from the EMs such as India. In this study, I methodically

focus on the relationship between sentiment and liquidity. For the purpose, I construct an aggregate sentiment index and examine the time varying nature of the sentiment and thus extend the current understanding of the nexus between investor sentiment and liquidity in a comprehensive and effective way. 3. Methodology I employ the univariate non-linear conditional heteroskedastic models to estimate monthly time-varying conditional liquidity and the investor sentiment. I apply Bollerslev’s (1986) generalized autoregressive conditional heteroskedastic models (GARCH), Nelson’s (1991) exponential GARCH and threshold GARCH models of Zakoian (1994) and Glosten et al. (1993) models. The present study is motivated to analyze the non-linear data generating process (Campbell and Hentschel, 1992) as one where the current value of the series is non-linearly related to the current and previous values of the error terms. This data generating process involves the comprehensive analysis of the salient features of volatility such as volatility clustering or pooling, volatility asymmetry, and capture the positive and negative asymmetry in terms of positive and negative news effect. The suitable volatility models to substantiate the objectives and to capture the essential volatility characteristics of sentiment for the stock market liquidity are GARCH (1, 1), EGARCH (1, 1) and TGARCH (2, 1). To capture the comprehensive volatility features of sentiment and its role in the volatility of liquidity, I introduce sentiment in the mean– variance framework. If sentiment is statistically significant in the non-linear GARCH framework models, I conclude that sentiment captures features of the volatility of stock market liquidity. Therefore, the study pertinently employs these GRACH class models. The prerequisite for univariate nonlinear models is to check for the persistence of serial correlation and the trend breaks in the time series of stock market liquidity and the conditional variance of the series. For diagnostics of serial correlation, I use ARCH-LM of Engle (1982), and McLeod and Li (1983) tests before and after the estimation of conditional models. To identify the trend break in the variance series, Iterative Cumulative Sum Square (ICSS) break test of Inclan and Tiao (2002) is carried out. 3.1. Conditional models with investor sentiment Given the significance of investor sentiment, I add it as an extra variable in both the mean and variance of the following GARCH class of models: 3.1.1. GARCH (1, 1) model with liquidity and investor sentiment LQt = α0 + β0 LQt −1 + β1 ASIt −1 + ut ht = ω0 +

q ∑ j=1

αj εt2−j +

p ∑

εt /Ω ∼ iid(0, ht )

β2 ht −i + β3 ASIt −1

(1) (2)

i=1

Here ω0 > 0 and αj + βi < 1 LQt represents the stock market liquidity whereas LQt −1 is the lagged values of stock market liquidity; ASIt −1 denotes the lagged sentiment of the market, ht is conditional variance. The β0 represents the coefficient of the lagged value of liquidity in the mean equation whereas the β1 denotes the coefficient of sentiment in the mean equation. The αj and βi are the coefficient of the lagged squared residuals and the lagged conditional variance respectively.

J. Kumari / Journal of Behavioral and Experimental Finance 23 (2019) 166–180

3.1.2. EGARCH (1, 1) model with liquidity and investor sentiment LQt = α0 + β0 LQt −1 + β1 ASIt −1 + ut N(0, 1) ∼ iid(0, ht )

(3)

q

( )⏐] [⏐ ⏐ ε ∑ εt −j ⏐⏐ ⏐ t −j log(ht ) = ω + αj ⏐ √ −E √ ⏐ ⏐ ht −j ht −j ⏐ m ∑ k=1

p

⏐ ⏐

q

∑ ∑ εt −k δk √ + βi ht −i + ψj ASIt −1 ht −k

i=1

ILQt and IASIt contain the information of the past and current observations of LQt and ASIt , respectively, and ‘∼’ denotes equivalence in distribution. l l Now consider LQt x = (LQt −lx −1,...., LQt ) and ASItx = (ASIt −lx −1,....., ASIt ) for lx , ly ≥ 1. If s = 1, then the null hypothesis in the Granger causality test can be written as follows:

⏐ ⏐

ly

l

ly

H0 : ASIt +1 ⏐(LQt x ; ASIt ) ∼ ASIt +1 ⏐ ASIt

j=1

+

169

(4)

j=1

where ω0 > 0, αj + βi < 1, δk < 0, if volatility is asymmetric. The LQt represents the liquidity and log(ht ) denotes log of conditional variance of liquidity proxies and sentiment index. The β is a vector of coefficient, εt white noise term and δi is asymmetric coefficient. The log of conditional variance makes the leverage effect exponential instead of quadratic, and therefore, the estimates of the conditional variance are guaranteed to be non-negative. Leverage effect is shown by δk < 0 if the impact of news is asymmetric. EGARCH model is highly effective in quantifying the magnitude of volatility, and persistence of the liquidity in the variance and leverage effect.

(8)

Assume Zt = Yt +1, then I have an invariant distribution vector ly l Kt = (LQt x , ASIt , Zt ). By assuming lx = ly = 1 and dropping the time indexes for simplicity, the joint and marginal probability density functions, under the null hypothesis, should fulfill the following relation: fx,y,z (x, y, z) fy (y)

=

fx,y (x, y) fy,z (y, z) fy (y)

.

(9)

fy (y)

Therefore, it can be shown that H0 can be expressed as E fx,y,z (x, y, z)fy (y) − fx,y (x, y)fy,z (y, z) = 0

[

]

(10)

which leads to the following statistics Tn (e) =

∧ n−1 ∑ ∧ (f X ,Y ,Z (LQi ASIi Zi )fy (ASIi ) n(n − 2) i

∧ ∧ −fX ,Y (LQi ASIi )fY ,Z (ASIi , Zi ))

3.1.3. TGARCH (2, 1) model with liquidity and investor sentiment

(11)

∧

LQt = α0 + β0 LQt −1 + β1 ASIt −1 + ut

N(0, 1) ∼ iid(0, ht )

ht = ω +

∑ i=1

q

αi εt2−i +

∑

βj ht −j + γ εt2−1 dt −1 + λ0 ASIt −1

(6)

n

j=1

where, dt = 1 if εt > 0, and otherwise. In this model, good news (εt > 0) and bad news (εt < 0) have different effects on the conditional variance. Good news has an impact of α , while bad news has an impact of (α + γ ). If γ = 0, the volatility is symmetric and if γ ̸ = 0, the volatility is asymmetric. λ0 component represents the coefficient of sentiment in the TGARCH model. 3.2. Nonlinear Granger causality tests- Hiemstra and Jones (1994) (H–J test) Diks and Panchenko (2006) (D–P) nonparametric approach Baek and Brock (1992) propose the non-parametric method to detect nonlinear Granger causality based on the correlation integral, which is a measure of the local spatial correlation of a time series. Hiemstra and Jones (1994) (H–J test) modify this model relaxing the assumptions of the independent and identically distributed series and mutual dependence. The non-linear Granger causality of Diks and Panchenko (2006) (D–P)—nonparametric technique is applied on the residuals of the estimated VAR models. Intuitively, the non-linear causality test verifies if the lagged value of one variable significantly explains the present value of another variable. The model assumes the time series as stationary. Applying the nonlinear Granger causality test to the residuals of the linear VAR model gives more information about the causality relationships between variables compared to that of the linear causality test. Moreover, this model captures the additional information in the residuals of the VAR model thus help predict the total distribution of the related variables which is not possible in the linear causality test. Diks and Panchenko (2006) (D–P) argue that if LQt Granger causes ASIt if for s ≥ 1: (ASIt +1,...., ASIt +s )/(ILQt , IASIt ) ∼ (ASIt +1,...., ASIt +s )/(IASIt )

(−dk ) fk (K (n − ∑i ) is aK local density estimator of Ki , f K (Ki ) = (2e) K 1) i,j̸ = i Iij where I(.) is an indicator function defined by Iij = −β   I( Ki − Kj < e) which e is the bandwidth such that e = Cn C > 0, 41 < β < 13 . According to Diks Panchenko (2006), the above-mentioned √ (Tand (e)−q) statistics satisfy: n n S D N(0, 1) where q and Sn are the esti-

−1

(5) p

∧

(7)

→

mator of asymptotic expectation and standard error, respectively. The H–J and the D–P test are the widely used methods to detect the nonlinear causal relationships (e.g. Alzahrani et al., 2014; Bekiros and S.D, 2014; Bampinas and Panagiotidis, 2015). Both the tests are nonparametric, which implies that the null hypothesis of no causality is tested against an unspecified alternative. 4. Data and variables The study period spans from the April-2000 to March-2018 (the 204 monthly time series observations). The sample is subject to the availability of data on variables to construct the ASI and liquidity variables. The data sources are NSE India, AMFI and the CMIE Prowess and Bloomberg terminal. 4.1. Liquidity variables and measurement I use 15 years of daily observations to measure the monthly liquidity variables. The measurement of liquidity is elusive and no single and unanimous method exists. Therefore, I employ four measures to capture the various dimensions of liquidity such as trading frequency, price-impact characteristics, and transaction costs. 4.1.1. Turnover rate (TR) The TR as a proxy of liquidity can be expressed as follows:

∑Dimd TRimd =

d=1

VOimd

(12)

NSOimd

∑D

imd where TRimd is the turnover rate, d=1 VOimd —monthly sum of the daily number of shares traded of the stock index, Nifty 50 (market portfolio), and NSOimd is the number of shares outstanding. This method is crude and intuitive as suggested by Datar et al. (1998).

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J. Kumari / Journal of Behavioral and Experimental Finance 23 (2019) 166–180 Table 1 Summary statistics.

4.1.2. Trading volume (TV)

Panel: A Summary statistics of market liquidity variables

D=imd

TVimd = ln(

∑

(VOimd Pimd ))

(13)

d=1

where TVimd is the traded volume of the Nifty Index. VOimd is the number of daily shares traded and Pimd is the daily price of the index values. In Eq. (10), i denotes the daily index values, d the number of days in a month and m the months. Therefore, the trading volume is calculated by the natural logarithm of the monthly sum of the daily product of the number of shares traded and their respective market price. The higher trading volume implies higher liquidity in the markets (Brennan et al., 1998). 4.1.3. Amihud’s (2002) illiquidity ratio Di

LIQ =

⏐

⏐

t i 1 ∑ ⏐Rtd ⏐

Dit

d=1

(14)

VOLitd

where Dit is the number of days in a month of the Nifty 50 Index. It assesses the average daily price impact caused by rupee trading volume for the index each month. To adjust the effect of inflation on the denominator, I scale the market illiquidity measure using the consumer price index (CPI). Following Amihud (2002), I use the logarithmic transformation of market liquidity. The illiquidity ratio explains the response of total returns to the rupee volume of the trading volume. Hasbrouck (2009) and Goyenko and Ukhov (2009) show the efficacy of the illiquidity ratio as a measure of price impact. This measure is essentially an illiquidity measure in the sense of Kyle (1985) which represents the response of price to the order flows. The method has been used in many of the studies to measure liquidity (e.g., Watanabe and Watanabe, 2008; Naes, 2004). 4.1.4. HL spread Hi − Low =

2(ea−1 )

(15)

1 + ea

√ √ √ ( 2β − β ) a= − γ /3 − 2 2 √ (3 − 2 2)

√

β = (Ln( γ = (Ln(

Ht

))2 + (Ln(

Lt Ht ,t +1 Lt ,t +1

Ht +1 Lt +1

))2

))2

(15.1) (15.2) (15.3)

where Ht and Lt are the daily high and low values. Corwin and Schultz (2012) develop this method to compute the Hi–Low (H–L) spread (the liquidity proxy) using the daily data of high and low prices. This method is a comprehensive measure of liquidity in a sense that it captures both the cross-sectional and the time series variations in the spreads of liquidity than that of the Hi–Low spread itself. 4.2. Properties of market liquidity The descriptive statistics of the liquidity variables presented in Table 1 show a considerable variation in the market liquidity over the period. The TR and TV proxies exhibit higher dispensation than that of LIQ and Hi–Low measures. All the market liquidity variables are non-normally distributed. All the liquidity variables are negatively correlated except the correlation between TR and Hi–Low measures, which is positive. Figs. 1 and 2 show that market liquidity essentially reflects anecdotal accounts of boom

Variables

Mean

Median

S. D

Min.

Max.

TR TV LIQ Hi–Low

0.153 0.120 0.001 0.021

0.119 0.097 0.000 0.020

0.127 0.108 0.005 0.005

0.023 0.013 0.031 0.000

1.626 1.334 0.998 0.048

Panel B. Correlations of market liquidity variables Variables

TR

TR TV LIQ Hi–Low

1

−0.004 −0.857 0.003

TV

LIQ

Hi–Low

1 0.000

1

1

−0.065 −0.976

Note: Panel A in this table shows the time-series summary statistics for the market liquidity variables. Panel B reports the correlation coefficients among market liquidity. Market liquidity variables are constructed as the time series average of the market index data for each trading day in the sample. The sample period extends from April 2000 to March 2018, with 6543 trading days and 216 months data. Trading Volume (TV) represents the trading volume of the stock index; the TV is the natural logarithm of the monthly sum of the daily product of the number of shares traded and their respective market price. Turnover rate (TR)—the number of shares traded divided by the number of shares outstanding; it represents the transaction cost characteristics of the liquidity. Amihud Illiquidity (LIQ) is defined as the log value of the product of total returns in response to the rupee volume of trading volume (Amihud, 2002). The market illiquidity measure is adjusted for inflation. Hi–Low spread estimator of Corwin and Schultz (2012) captures the bid–ask spread of the liquidity. S.D refers to the standard deviation.

and crashes. For instance, liquidity represented by TV, TR, LIQ, and Hi–Low is low during the mid-2000 and 2007 due to technology crash and global financial crisis respectively. In turn, it directly implies that negative shocks reduce market liquidity and vice versa. 4.3. Aggregate sentiment index (ASI) Our choice of ASI is based on Brown and Cliff (2004), Baker and Wurgler (2006) and Verma and Soydemir (2009). I employ the following prominent macroeconomic fundamentals to remove the redundant business cycle information. The index of industrial production (IIP) and Treasury bill rates are proxy for short-term interest rates (TBR) and economic growth respectively. I also use exchange rate (Rupee/Dollar) (EX), inflation (INF) and foreign institutional investment (FII) as sensitive business cycle proxies. Among the market wide systematic risk factors, I select excess returns on the market portfolio (Rm − Rf ), the premium on a portfolio of small stocks relative to large stocks (SMB), the premium on a portfolio of high book/market stocks relative to low book/market stocks (HML) and momentum factor (WML). I follow Fama and French (1993), Jegadeesh and Titman (1993) and Carhart (1997) in the factor loadings namely Rm − Rf , SMB, HML and WML as the systematic risk factors in the construction of ASI for India. 4.3.1. Theoretical framework and construction of ASI The modern theories of finance build on the argument that noise traders are unimportant in the financial asset pricing and risk–return trade-off process because trades are always made by rational arbitrageurs (Friedman, 1953; Fama, 1965). However, the behavioral theory of finance paradigm poses challenges to the assumptions and propositions of the neoclassical school. The noise traders’ framework of De Long et al. (DSSW) (1991) and irrational exuberance approach of Shiller’s (2000) assert that irrational arbitrageurs trade against market fundamentals driving the prices away from the intrinsic value. Behavioral theories posit certain plausible features of assets which are interpreted

J. Kumari / Journal of Behavioral and Experimental Finance 23 (2019) 166–180

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Fig. 1. Time series patterns of the liquidity variables. Note: The figure shows the time series trend of the four liquidity variables namely turnover rate (TR), trading volume (TV), the Amihud (2002) illiquidity ratio (LIQ), and the Hi–Low spread estimator (Corwin and Schultz, 2012).

Fig. 2. Co-movement of the liquidity variables. Note: Figure represents the co-movement of the liquidity variables namely trading volume (TV), turnover rate (TR), Amihud Illiquidity measure (LIQ) and the High–Low spread estimator for bid–ask spread (Hi–Low spread). The graphical representation captures the historical movements of the variables and reveals that the variables follow a similar trend.

as deviations from fundamental values and that the traders who bring these deviations are not fully rational and termed as noise traders (Barberis and Thaler, 2003). More comprehensively, the rapid rise and fall in asset prices are subject to investor sentiment which is prone to bullish and bearish nature of the investors (Baker and Wurgler, 2006, 2007). The noise traders trade on noisy signals (unusually bullish or bearish) affect the asset prices and make the markets volatile. Black (1986) was first to provide a model of noise traders or investor sentiment in asset prices. It was further extended by researchers like Shefrin and Statman (1985), Shleifer and Summers (1990), Lakonishok et al. (1992), Campbell and Kyle (1993), Palomino (1996), Barberis and Shleifer (1998), Daniel et al. (1998) and Hong and Stein (1999). According to Baker and Wurgler (2007), stocks which are young with less market capitalization, unprofitable, highly volatile, non-dividend paying, distress firms, and the extreme growth seeking firms are broadly affected by the waves of sentiment. The DSSW (1990) model contemporaneously asserts the relationship between sentiment and price volatility at the level of individual securities. More the irrational arbitrageurs trade on noisy signals, higher the increase in price volatility. By introducing demand shifts driven by irrational speculation and binding arbitrage constraints, sentiment can influence volatility and liquidity.

The behavioral finance theorists have attempted to define investor sentiment and more emphatically, the quantification of investor sentiment. The theoretical and practical applicationoriented proxies of sentiment are based on psychological biases and beliefs. Primarily, researchers and financial analysts use the annotation of sentiment in wide spectrum varieties. With the seminal paper of Baker and Wurgler (2006, 2007), the quantification of investor sentiment has taken a new shift from conventional approach because they introduce the ‘‘top-down’’ and ‘‘bottom-up’’ approaches to measure sentiment. The bottom-up approach uses the individual investors’ psychological biases such as overconfidence, representativeness, and conservatism to explain how individual investor reacts to past returns or fundamentals.2 The bottom-up approach is microscopic in nature. In contrast, the top-down approach is macroeconomic and derived from the reduced form of measurement; and aggregate sentiment proxy traces the effect of market returns and volatility. I employ the top down macroscopic approach to construct ASI for India. The institutional investors dominate the Indian stock market 2 See, Barberis and Shleifer (1998) and Daniel et al. (1998) for these models.

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and hence, the bottom-up approach based on individual survey measure is inapplicable to the EMs such as India. Aitken (1998) was first to study institutional investor sentiment in the wake of liberalization in EMs. The study reveals that EMs are more prone to the bubbles & crashes, and inefficient in the sense that prices do not always reflect all relevant information. Employing the conventional variance ratio test, the study finds that EMs experienced a sharp increase in autocorrelation in total returns when institutional investors expand their holdings significantly in these markets. Zygadlo et al. (2015) employ the Thomson Reuters Market Psych Indexes to investigate the contemporaneous relationship between sentiment/optimism and excess returns at the aggregate level in EMs. The univocal findings suggest a positive contemporaneous relationship between investors’ moods and excess returns only in Brazil and China. The authors also show that excess returns are more sensitive to changes in investors’ moods during periods of negative sentiment/optimism index values in four out of eight markets researched. In the similar veins, Corredor et al. (2015) empirically probe the role of investor sentiment in stock markets of the Czech Republic, Hungary, and Poland. They employ consumer confidence (CC) to measure sentiment. The results show that greater impact of sentiment on stock price movement. The hitherto literature prominently focuses on the individual measurement of investor sentiment which represents the individual component of the investor sentiment. The recent behavioral finance literature defines the investor sentiment as the propensity to speculate and there is no perfect and composite measure which captures the common component of the several sentiment dimensions. The role of investor sentiment in the EMs stock market is explored before with different perspective (e.g. Ogunmuyiwa, 2010; Lin, 2015; Kumari and Mahakud, 2016; Debata et al., 2017). These studies in the context of EMs have followed the same method which is less relevant to the EMs such as India because of the dominance of institutional investors. Besides, the sentiment was confined to certain indices which hardly capture the heterogeneity among the EMs. The current study is comprehensive to date as it employs the sentiment index which captures the role of all the market related variables partially in the form of aggregate sentiment index. Therefore, I adopt the top-down approach of Baker and Wurgler (2006, 2007) and Verma and Soydemir (2009). I employ ten indirect aggregate investor sentiment measurements for the ASI construction. The ASI represents the entire market sentiment. I identify four categories of market-related sentiment variables that influence the stock prices: market performance, type of trading, derivatives, and the other sentiment proxies. The advances and decline ratio (ADV/DEC) is the most important technical indicator among the variables in the market performance category. The ADV/DEC is the ratio of the number of advancing issues to the number of declining issues (Brown and Cliff, 2004). The rising (declining) trends of the ADR confirm the upward (downward) trend of the market (Brown and Cliff, 2004). Theoretically, ADV/DEC is positively related to sentiment. Our second proxy is a buy–sell imbalance (BSI) ratio—the ratio of the total volume of buy minus the total volume of sell to the total volume of buy plus the total volume of sell (Kumar and Lee, 2006). Theoretically, BSI and the sentiment are positively associated. Turnover volatility ratio (TVR) of Datar et al. (1998) represents the market liquidity (Jun and Shawky, 2003). Turnover ratio is the ratio of trading volume and market capitalization. The TVR is the turnover ratio divided by the standard deviation of the market returns. Several widely acclaimed variables such as bid– ask spread, return reversals (Pastor and Stambaugh, 2001), and illiquidity ratio (Amihud, 2002) can represent market liquidity. Nevertheless, I select the TVR as market liquidity proxy to understand the fundamental relations between liquidity and market

stock prices and returns. In any market with short sales constraints, irrational investors participate, and thus add liquidity only when they are optimistic; hence, high liquidity is a symptom of overvaluation. Our next proxy is related to the performance of IPO markets; these IPO markets are always and profoundly sentiment prone. The first day IPO numbers are the indicator of investors’ enthusiasm for the future performance of firms. I take the first day IPO numbers as a proxy of investor sentiment. The share of equity issues in total equity and debt issues is another measure of financing activity that captures the sentiment. Baker and Wurgler (2000) find that high values of the equity share predict low market returns. The equity share is defined as gross equity issuance divided by gross equity plus gross longterm debt issuance. A higher value of equity issuance in total debt and equity considered as bullishness of the investors. Our sixth variable of investor sentiment is Div. P, which is used in the behavioral finance literature as an indirect measure of sentiment. Notably, Div.P is the log difference of the average market-to-book ratio of dividend payers and non-payers. Mainly the young and small size, low profitable and low-growth opportunity firms announce dividends for the better prospect of the firms. Therefore, the steep increase in Div. P is the explicit indication of a negative relationship with the investor sentiment. I choose percentage change in margin borrowing based on the type of trading as one of sentiment variable. The margin borrowing (∆ Margin) implies taking trading positions in the markets with borrowed funds. The margin traders’ borrowing indicates the bullish nature of investors and thus suggests a positive relationship with the sentiment (Brown and Cliff, 2004). The put–call ratio (PCV) is a measure of market participants’ sentiment derived from derivate instruments. The PCV is the ratio of the trading volume of put options to the trading volume of call options. When market participants are bearish, they buy put options either to hedge their spot positions or speculate on bearish expectations. Therefore, when the trading volume of put options is larger than that of the call options, the ratio goes up and vice versa (Brown and Cliff, 2004; Wang et al., 2006; Finter et al., 2011). I employed a net purchase of a mutual fund as a proxy for fund flows (Fund Flow). Neal and Wheatley (1998), and Brown and Cliff (2004) find this indicator helpful in predicting the premium of small stocks over large stocks. 4.3.2. Market-related ASI I construct the ASI following Baker and Wurgler (2006, 2007). In our first approach, I employ ten indirect measures of sentiment proxies namely ADR, BSI, TVR, TV, IPO, equity issues in a total of equity and debt, Div. P, PCR, ∆ Margin and fund flow. In the first step, I create an index taking the first principal component of these ten indirect measures and the lagged components of these sentiment variables. In the second step, I compute the correlation between the indexes constructed in the first step and the lead and lag values of the indirect sentiment measures. Finally, I calculate the index taking the difference between step one and step two. In our second approach, following Baker and Wurgler (2006), I go for orthogonalization of the sentiment proxies. It is likely that certain sentiment proxies described in the preceding discussion are related to the present economic phenomenon. To isolate and ensure that our findings are not driven by the fluctuations in macroeconomic fundamentals, I adjust our sentiment proxies for the business cycle fluctuations. I employ business cycle variables namely economic growth, interest rate, term spread, exchange rate, inflation and FII to remove the business cycle component from the computed sentiment index. Apart from the economic

Table 2 Descriptive statistics and correlations. Table 1 Panel A Descriptive statistics and contemporaneous correlations of raw proxies Mean 0.924 0.004 1.841 0.152 0.139 3.826 0.011 0.817 3.622 0.298

Std. Error 0.016 0.003 0.420 0.017 0.018 0.303 0.011 0.015 0.023 0.016

S. D 0.214 0.045 5.433 0.219 0.236 3.927 0.146 0.203 0.305 0.215

Variance 0.045 0.002 29.52 0.048 0.056 15.421 0.021 0.041 0.093 0.046

Kurtosis 1.184 2.917 38.446 6.489 4.641 2.624 21.636 −0.340 −0.816 3.102

Skewness

Minimum

0.782

0.55

−0.080

−0.164 −1.617

6.168 2.247 1.938 1.541 2.951 0.350 −0.406 1.546

0

−0.334 0

−0.453 0.331 2.910 0.0300

Maximum

Index

1.8 0.174 39.671 1.353 1.237 19 1.132 1.35 4.181 1.314

1 0.73 0.25 −0.06 −0.05 0.06 −0.04 0.10 0.09 0.11 −0.04

ADR

BSI

DivP

EI

FF

IPOs

Margin

PCR

TV

TVR

0.461 0.375 −0.218

1 0.229 0.060 0.088 0.041

1 0.085 0.025 0.125

1 0.564 −0.342

−0.626

1

FF

IPOs

Margin

PCR

TV

TVR

1 0.276 0.056 0.142 0.021

1 0.110 0.059 0.092

1 0.580 0.334

1 0.643

1

1

−0.17 −0.09 −0.10 0.09 −0.14 0.02 −0.01 −0.04 −0.03

1 0.031 −0.155 −0.229 0.028 −0.023 −0.269 −0.033 −0.109

ADR

BSI

1

−0.003 0.179 −0.067 −0.051 0.355 0.213 −0.200

1 0.242 0.177 0.116 0.388 0.394 −0.181

DivP

EI

1

−0.043 −0.097

1

Panel B Descriptive statistics and contemporaneous correlations of orthogonalized proxies Mean Index ADR BSI Div.P EI FF IPOs Margin PCR TV TVR

0.0021 0.1232 0.2136 0.8764 0.2876 0.9876 0.2486 0.2316 0.6542 0.2436

St. Error 0.0145 0.0033 0.3976 0.0168 0.0169 0.2714 0.0110 0.015 0.0227 0.0158

S.D 0.1880 0.0427 5.1381 0.2179 0.2192 3.5077 0.1423 0.1984 0.2945 0.2044

Variance 0.0353 0.0018 26.400 0.0475 0.0480 12.304 0.0202 0.0394 0.0867 0.0418

Kurtosis 0.3245 2.6227 33.061 6.7429 4.9962 1.5337 21.763 −0.407 −0.760 1.5309

Skewness 0.4146 0.1114 5.4291 2.2558 1.7843 1.0914 2.982 0.304 −0.216 1.0416

Minimum

−0.3791 −0.144 −6.7760 −0.2120 −0.559 −5.882 −0.440 −0.459 −0.6627 −0.4453

Maximum

Index

0.6227 0.1849 36.860 1.2077 1.0615 13.033 1.0920 0.5301 0.6440 0.7421

1 0.066 0.026 −0.014 −0.040 −0.005 −0.143 −0.019 −0.039 −0.032 0.770

1

−0.119

1

0.048 −0.108 0.029 −0.134 −0.020 0.032 −0.042 −0.081

−0.002 −0.162 −0.218 0.081 −0.033 −0.306 −0.045 −0.072

1

−0.018 0.158 −0.082 −0.020 0.353 0.222 0.195

1 0.232 0.216 0.133 0.382 0.394 0.185

1

−0.099 −0.044 0.463 0.409 0.246

Note: Table presents the summary statistics for all raw and orthogonalized monthly market-wide sentiment variables. The ADV/DEC is the ratio of the number of advancing issues to the number of declining issues (Brown and Cliff, 2004). Buy–sell imbalance (BSI) ratio is the ratio of the total volume of buy minus the total volume of sell to the total volume of buy plus the total volume of sell (Kumar and Lee, 2006). Div.P is the log difference of the average market-to-book ratio of dividend payers and non-payers. The share of equity issues in total equity and debt issues is another measure of financing activity that captures the sentiment. Baker and Wurgler (2000) find that high values of the equity share predict low market returns. The equity share is defined as gross equity issuance divided by gross equity plus gross long-term debt issuance. Net purchase of a mutual fund is used as a proxy for fund flows (Fund Flow). The first day IPO numbers are the indicator of investors’ enthusiasm for the future performance of firms. I take the first day IPO numbers as a proxy of investor sentiment. I choose percentage change in margin borrowing based on the type of trading as one of sentiment variable. The margin borrowing (∆ Margin) implies taking trading positions in the markets with borrowed funds. The margin traders’ borrowing indicates the bullish nature of investor and thus suggests a positive relationship with the sentiment (Brown and Cliff, 2004). The put–call ratio (PCR) is a measure of market participants’ sentiment derived from derivate instruments. The PVC is the ratio of the trading volume of put options to the trading volume of call options. Turnover ratio is the ratio of trading volume and market capitalization. The TVR is the turnover ratio divided by the standard deviation of the market returns. S.D denotes standard deviation.

J. Kumari / Journal of Behavioral and Experimental Finance 23 (2019) 166–180

Index ADR BSI Div.P EI FF IPOs Margin PCR TV TVR

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fundamentals, the standard asset-pricing models proclaim the significant role of specific market wide systematic risk factor loadings in explaining the business cycle fluctuations. Hence, I incorporate Rm − Rf , SMB, HML, and WML as four market wide systematic risk factor loadings to construct the ASI. To compute the ASI in the first step, I need to regress, each sentiment proxies on the ten economic fundamentals. To orthogonalize sentiment indicators, I estimate a regression for each sentiment indicator separately. In the second step, I obtain the residuals of each ten regressions and treat them as better proxies. I obtain the residuals from the first step regression and use them in the subsequent analysis as the orthogonalized sentiment proxies. I estimate Eq. (16) to eliminate the redundant effect of macroeconomic variables and the market wide systematic risk factor loadings: Sentit = α0 + γj

J ∑

Fundjt + εit

(16)

j=1

In Eq. (13), α0 is constant, γj is parameter needs to be estimated, Sentit is sentiment proxies in each regression. Fundjt represent the set of ten explanatory macroeconomic factors and market-wide systematic risk factor loading variables. εit represents the random errors obtained from each regression equation. The fitted values from the regression model explain the rational component of the investor sentiment index whereas the residuals capture the irrational component of the sentiment index. To construct ASI, I use several proxies described in the preceding paragraph. However, the mentioned variables capture the plausible and naive part of the sentiment. Possibly, I may be left with some redundant idiosyncratic component or non-sentiment related components even after adjusting for macroeconomic variables. To circumvent such problem, I use the first principle component out of ten variables and the lagged values of the variables to ensure that all the sentiment indicators partially capture the aspect of the investors’ attitude and irrational behavior. I use the first principal component analysis of the residuals obtained from the regression estimation in the first step. Each respective proxy’s lead or lag, whichever has a higher correlation with the firststage index rescaling the coefficients so that the index has unit variance, I choose it for the sentiment index. Following Eq. (16) the procedure leads to parsimonious sentiment index coefficients estimated using the first principal component of each of the ten fundamental-orthogonalized sentiment proxy variables. ASIt = 0.203ADRt −1 + 0.020BSI − 0.492Div.Pt −1 + 0.162EI

+0.026FFt −1 + 0.238IPOs + 0.097∆MARGIN − 0.062PCR +0.030TVt −1 + 0.225TVRt −1 (17) The first principal component explains the 51% of the sample variance, and hence I can conclude that one factor captures much of the common variation. The descriptive statistics of raw sentiment proxies, orthogonalized proxies, the correlation matrix of sentiment indicators with market index and correlation among the variables are presented in Table 2. Cross-correlation matrix suggests that all of the sentiment proxies are correlated in the desired direction indicating a common component of investor sentiment explained by these all variables. Panel B of Table 2 presents the descriptive statistics and cross-correlations of orthogonalized sentiment variables further employed in the construction of ASI. In Table 3, I present the descriptive statistics and crosscorrelations of the market wide systematic risk factors involved in the regression analysis process for the orthogonalization to eliminate the redundant effect of macroeconomic or business cycle proxies in the sentiment index. The correlation between

macroeconomic fundamentals and the market wide systematic risk factors and the ASI shows that macroeconomic factors are correlated with the sentiment index. Figs. 3 and 4 exhibit the joint movement of sentiment index and the market index. Fig. 5 suggests that the ASI explains the time variation in the market liquidity variables. Moreover, the co-movement plots indicate that liquidity and ASI capture the anecdotal shifts of booms and crashes in the economy and exhibit the bearish trend when the economy enters into the downward swing and vice versa. The market liquidity and sentiment together capture the upswings and downswings in the Indian economy. 5. Empirical findings and discussions 5.1. GARCH estimates The unit root statistics presented in Table 4 confirm that all the variables are stationary. The results presented in Table 5 indicate the presence of ARCH effect in the market-related liquidity variables and the ASI. Further, Inclan and Tiao (2002) structural break test is carried out to check the sudden shifts and trend break in the liquidity variables and ASI. Nevertheless, the test results suggest no such breaks in the series to use the dummy variables in the GARCH class of models. I estimate three state-of-art non-linear GARCH class models to examine the predictability and interdependence between the market liquidity and the ASI. I estimate the GARCH (1, 1), EGARCH (1, 1) and TGARCH (2, 1) with and without ASI in the mean–variance framework.3 This study is the first of its kind to employ the non-linear conditional volatility models to analyze the volatility persistence among the liquidity variables. Further, the study introduces ASI in the mean and the conditional variance equations to examine whether sentiment predicts the liquidity. The estimates of the GARCH (1, 1), EGARCH (1, 1) and the TGARCH (2, 1) models without ASI presented in Table 6 show the volatility persistence among all the market-related liquidity variables. The ASI in the mean and conditional variance equations show a significant impact of sentiment on the Indian stock market liquidity. The symmetric GARCH (1, 1) model estimates suggest non-zero significant values for all the liquidity variables namely TV, TR, LIQ, and the Hi–Low indicating that volatility persistence among these variables. Essentially, the coefficients of ARCH (α ) and the GARCH (β ) are non-zero positive significant values for all the liquidity variables indicating that the lagged values of the liquidity variables and the lagged values of the non-linear conditional variance capture the volatility of the market liquidity. Moreover, the value of α + β for TV, TVR, LIQ and the Hi–Low close to one indicate the high degree of the volatility persistence. Therefore, the symmetric GARCH model captures the volatility persistence and the volatility clustering efficiently. The estimates of EGARCH (1, 1) shows the presence of the volatility asymmetry as δk < 0 for the TV, TVR, LIQ, and Hi–Low. The asymmetric volatility implies that negative shocks of the same magnitude compared to that of positive shocks influence the stock market liquidity. The investors are more prone to negative shocks which further affect their trading decisions and the overall market liquidity. In other words, the result implies that the volatility spillover mechanism is asymmetric. The estimates of TGARCH (2, 1) reveal that the news impact is asymmetric because γ ̸ = 0. The results are consistent with 3 We specify the GARCH models after testing the order of an ARCH (p ) model employing the LM test as mentioned in the previous section. In the present study, we use the AR residuals of the monthly stock returns regressed on a constant term and past lagged residuals values. The selection of lag length along with the log likelihood value is based on the order of the process that changes in the lag values until it becomes insignificant.

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175

Table 3 Descriptive statistics and cross-correlations of business cycle proxies and market-wide systematic risk factor loadings. Panel A Descriptive statistics of ASI, business cycle proxies and market-wide systematic risk factor loadings

Mean Median S.D Kurtosis Skewness Min Max

ASI

EX

FII

INF

TBR

Term

IIP

Rm-Rf

SMB

HML

WML

0.01 0.00 0.03 3.45 0.11 −24.85 12.56

0.00 0.00 0.02 2.68 0.42 −0.06 0.08

0.01 0.06 1.22 6.03 0.36 −5.46 6.52

0.00 0.00 0.00 1.59 0.07 −0.01 0.02

6.55 6.62 1.82 −0.64 0.10 3.11 11.14

1.26 1.18 1.19 1.25 0.44 −2.66 4.64

0.00 0.00 0.08 44.14 0.14 −0.64 0.66

−0.21 −0.21

−0.12 −0.06

−0.40 −0.36

0.06 −0.44 −0.27 −0.37 −0.08

1.07 4.01 0.52 −3.40 4.85

0.03 0.00 0.79 1.39 0.01 −2.35 2.56

1.01 2.92 0.60 −3.33 4.19

TBR

Term

IIP

Rm-Rf

SMB

HML

WML

Panel B Correlation matrix of ASI and business cycle proxies ASI ASI EX FII INF TVR Term IIP Rm-Rf SMB HML WML

EX

FII

INF

1

−0.29 0.10 −0.00 −0.01 0.00 0.02 0.02 −0.04 −0.01 0.01

1

−0.24 0.00 0.21 −0.17 −0.00 −0.18 0.11 −0.03 −0.05

1

−0.07 −0.04 0.01 0.05 0.03 0.05 −0.05 −0.01

1 0.05 0.09 −0.17 −0.04 −0.08 −0.05 0.01

1

−0.64 −0.08 −0.97 0.05 −0.03 0.08

1

−0.03 0.62 0.02 −0.01 0.00

1 0.08 0.03 0.02 0.11

1

−0.06

1

0.03 −0.08

−0.53 0.19

1

−0.12

1

Note: Descriptive statistics show the fundamental macroeconomic proxies and market-wide systematic risk factor loadings. ASI denotes aggregate sentiment index, EX the rupee-dollar exchange rate and FII the foreign institutional investors. TBR, Term, and IIP denote Treasury bill rate, Treasury long term rate and Index of Industrial Production respectively. The excess returns on the market portfolio (Rm-Rf), the premium on a portfolio of small stocks relative to large stocks (SMB), the premium on a portfolio of high book/market stocks relative to low book/market stocks (HML) and momentum factor (WML) are the systematic risk factors employed to develop of ASI for India. The correlation between ASI, the macroeconomic fundamentals, and the market-wide systematic risk factors are presented in Panel B.

Fig. 3. Aggregate sentiment index. Note: The figure represents the ASI obtained from the PCA after the orthogonalization process to remove the macroeconomic variables, business cycle proxies, and market-wide systematics risk factors.

Fig. 4. Co-movement of ASI and Nifty 50.

the EGARCH model as γ is either γ < 0 and γ > 0 for different variables. The values of TV, TVR, LIQ, and Hi–Low are less than zero and thus exhibit that the negative shocks to the conditional variance persist for a longer time than the positive shocks. It implies that the volatility of market liquidity is more aggravated through the negative risk factors in the markets. The presence of negative news supports the leverage effect in the liquidity variables. Overall, the findings suggest that past liquidity play a

significant role in determining future market liquidity. The insignificant ARCH statistics on residuals indicate that these models capture the persistence of volatility appropriately. The McLeod and Li (1983) statistics also indicate no autocorrelation in the residuals and squared residuals drawn from the three GARCH models. Further, I estimate three separate non-linear GARCH class of models by introducing ASI in the mean and the conditional

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Fig. 5. Co-movement of ASI and market liquidity variables. Note: The plots show the co-movement of ASI and the market liquidity variables as defined in Table 1. The figures indicate the positive trend between sentiment and liquidity. Table 4 Unit root tests statistics. Variables

TV LIQ TVR Hi–Low ASI

ADF

PP

KPSS

Without trend

With trend

Without trend

With trend

Without trend

With trend

−12.567* −13.386* −15.043* −15.865* −20.928*

−12.566* −13.365* −15.113* −15.836* −20.758*

−13.688*

−13.693* −13.505* −14.221* −11.823* −29.899*

0.088 0.103 0.233 0.124 0.030

0.070 0.073 0.061 0.111 0.020

13.492* −14.114* −11.821* −29.873*

Note: Variable are as defined in Table 1 and Table 2. The table reports the ADF, PP and KPSS tests statistics. The optimal lag for the ADF test and truncation lag for PP test are selected based on the AIC and SIC criteria. In the case of both ADF and PP tests, the critical values at 1%, 5%, and 10% are −3.46, −2.87 and −2.57, respectively for the model without trend and −4.00, −3.43 and −3.13 for the model with the trend. ADF and PP tests examine the null hypothesis of a unit root against the stationary alternative. For fixing the truncation lag for the KPSS test, spectral estimation methods selected are the Bartlett kernel, and for bandwidth, the Newey–West method. The critical values at 1%, 5% and 10% are 0.73, 0.46 and 0.34, respectively for the model without trend and 0.21, 0.14 and 0.11 for the model with trend. The KPSS test examines the null of stationary. *Indicates significant at 1% level. Table 5 ARCH-LM test statistic. Variables

LM statistic

P-values

TV LIQ TVR Hi–Low ASI

6.36* 10.17* 5.68* 44.63* 18.29*

0.00 0.00 0.00 0.00 0.00

*Indicate the ARCH effect for all variables at 1% level of significance.

variance equations to capture the impact of ASI on the market liquidity. The estimates presented in Table 6 reveal that ASI has a positive and negative impact on the overall stock market liquidity. The statistically significant coefficients of GARCH (1, 1) model shows that ASI has a negative impact on the TV and positive impact on the TVR, LIQ and the Hi–Low liquidity variables in the mean equation. In the same vein, I find ASI has the positive impact on all liquidity variables such as TV, TVR, LIQ and Hi–Low ratio implying that bullish (bearish) sentiment creates the higher (lower) market liquidity. The findings, hence, support the theoretical proposition of behavioral finance that sentiment affects the market liquidity through the noise traders and the irrational market makers channels. Also, the significant coefficients of ASI in the mean and variance equation suggest that ASI efficiently captures the volatility persistence and clustering of market liquidity. The results imply that past psychological biases,

optimism and wishful thinking, representativeness and anchoring and conservatism of investors affect the stock market liquidity. Further, the estimates of EGARCH (1, 1) which incorporates the ASI in the mean and conditional variance equation show that ASI is negative and significant for all liquidity variables in the mean equation. It implies that the bearish sentiment of the investors supports the volatility asymmetry characteristics of market liquidity. Further, the conditional variance equation coefficients reveal that ASI is statistically significant and responsive to the asymmetry effect. The result implies that heuristic biases drive the institutional investors who dominate EMs such as India. These biases of institutional investors lead to a decline in average market liquidity in India. Our present finding supports the proposition of behavioral school that the liquidity of the market is more prone to the shift in investor sentiment. Our evidence is dissimilar from the US and other developed markets in which the individual investors are termed as noise traders and institutional investors as rational arbitrageurs. However, the institutional investors act as noise traders in EMs such as India. Given their dominance in the EMs, they influence the market liquidity through the non-fundamental information. Our results further suggest that past sentiment has a positive impact on current market liquidity and therefore, negative sentiment reduces market liquidity. When institutional investors are pessimistic about the stock market trend, they trade less and thus market liquidity declines. I estimate the TGARCH (2, 1) to find out the impact of positive and negatives news on the stock market liquidity. The results

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177

Table 6 Non-Linear GARCH estimates with and without sentiment in the mean-variance framework. Panel: A Non-linear GARCH models estimates without sentiment in the mean–variance framework for market liquidity GARCH model estimates TV

EGARCH model estimates

LIQ

ω α β α+β δ γ

0.005 0.083* 0.851* 0.934* – – ARCH-LM 4.18(0.52) ARCH-LM2 2.310(0.80) LL 197.92 SIC −2.21 Mcleod Li Q(20) 22.88 Mcleod Li Q(40) 44.29

TVR

−0.005

0.002 0.442* 0.105* 0.523* 0.843* 0.965* 0.948* – – – – 18.66(0.00) 3.84(0.53) 12.45(0.02) 5.757(0.33) 322.09 202.45 −3.28 −2.26 81.25 26.28 183.85 51.02

TGARCH model estimates

Hi–Low

TV

LIQ

TVR

Hi–Low

0.004 0.293* 0.645** 0.938* – – 4.01(0.54) 7.68(0.17) 234.51 −2.21 22.33 31.14

−2.509

−7.348

−2.537

TV

LIQ

−1.948

0.020 0.339** 1.018 0.353** 0.384** 0.112** 0.564** −0.061 0.565** 0.579** 0.854* 0.903* 0.957* 0.918* 0.963* 0.966* −0.105* −0.346* −0.152* −0.095* – – – – −0.037* 4.02(0.54) 2.07(0.72) 2.824(0.72) 0.27(0.99) 4.76(0.44) 1.499(0.91) 7.24(0.12) 1.748(0.88) 0.17(0.99) 1.30(0.93) 200.04 332.56 203.11 127.00 202.21 −2.17 −3.39 −2.21 −1.83 −2.20 25.15 100.57 28.58 1.81 30.52 50.13 231.41 56.72 1.99 44.78

TVR

Hi–Low

4.19 0.133** 0.812* 0.945*

0.003 0.114** 0.849* 0.963* – 0.261* −0.023* 3.04(0.69) 3.45(0.63) 1.20(0.94) 5.78(0.32) 543.79 202.48 −5.30 −2.23 2.29 25.59 6.64 49.57

7.71 0.105** 0.200** 0.305**

−4.342

−3.342

−0.371* 1.25(0.93) 0.27(0.99) 645.37 −6.32 35.68 37.05

Panel: B Non-linear GARCH estimates with the ASI in the mean–variance framework for market liquidity

ω

−6.081 −0.015*

ASI

α β α+β

0.982* 0.001* 0.999* ASI 0.222* δ – γ – ARCH-LM 1.28(0.93) ARCH-LM2 0.86(0.97) LL 298.20 SIC −2.00 Mcleod Li Q(20) 5.70 Mcleod Li Q(40) 19.57

−3.456

−6.164

0.343* 0.652* 0.263* 0.915* 0.345 – – 2.45(0.90 0.76(0.96) 234.67 −2.67 6.00 17.67

0.041* 0.172* 0.762* 0.934* 0.051* – – 1.29(0.93) 0.55(0.99) 297.96 −1.90 5.04 18.34

−5.345 0.453 0.210* 0.723* 0.933* 0.045 – – 2.33(0.92) 0.62(0.90) 267.56 −2.00 6.00 15.35

−6.166 −0.020*

−5.342 −0.456

−0.012 −0.021*

0.345* 0.555* 0.900* −0.001* −0.164 – 1.28(0.93) 0.83(0.97) 294.98 −2.13 6.00 18.57

0.345* 0.523* 0.868* −0.234 −0.238 – 1.34(0.90) 1.24(0.97) 202.87 −2.90 6.34 16.67

0.369* 0.466* 0.835* −0.521* −0.166 – 2.29(0.94) 0.55(0.99) 292.69 −2.13 7.04 20.22

−5.081 −0.015*

−0.257 −0.018*

0.756 0.942* 0.100* 0.345* 0.001* 0.800* 0.623 0.943* 0.900* 0.968* 0.222* 0.014* −0.234 −0.278 – – – −0.072 −0.238 1.28(0.93) 2.34(0.96) 3.24(0.92) 0.86(0.97) 0.76(0.76) 0.70(0.75) 298.20 203.77 201.67 −2.00 −2.20 −2.14 5.70 10.23 7.56 20.20 34.65 30.17

−0.252 −0.180* 0.100* 0.793* 0.893* 0.015* – −0.063 1.34(0.90) 1.24(0.97) 202.87 −2.90 6.34 28.54

0.656 0.445* 0.523* 0.968* −0.234 – −0.237 1.99(0.80) 2.34(0.90) 203.89 −2.78 6.00 28.65

Note: In this table, ω denotes the constant term, α the ARCH term. The β is the GARCH term and α + β represent the stationary condition of model and volatility persistence. The coefficient of the GARCH, EGARCH and TGARCH models are reported here. ASI represents the aggregate sentiment index introduced in the mean and the variance framework. The values in the parenthesis in ARCH-LM tests show the respective p-values. *Denote the significance level at 1%. **Denote the significance level at 5%. Table 7 Nonlinear causality statistics for ASI → TV and ASI → TVR. Relation

ASI → TV

Lags lx = ly

1

TV → ASI 2

ASI → TVR

TVR → ASI

3

4

1

2

3

4

1

2

3

4

1

2

3

4

0.001* 0.657

0.017* 0.012*

0.002* 0.032*

0.028* 0.865

0.071 0.954

0.024* 0.234

0.007* 0.004*

0.003* 0.425

0.001* 0.023*

0.046* 0.035*

0.276 0.987

0.125* 0.012*

0.045* 0.001*

0.055 0.032*

0.164 0.052*

0.020* 0.043*

0.027* 0.011*

0.012* 0.056*

0.004* 0.003*

0.001* 0.001*

0.006* 0.002*

0.008* 0.012*

0.876 0.045*

0.567 0.003*

0.456 0.765

0.765 0.766

0.876 0.876

0.023* 0.023

0.039* 0.003

0.002* 0.042

0.042* 0.033

0.987 0.042

0.654 0.072

0.003* 0.654

0.001* 0.023

0.003* 0.065

0.025* 0.004

0.013* 0.987

0.012* 0.567

0.003* 0.002

0.001* 0.006*

0.034* 0.024*

0.432 0.065

0.842 0.065

0.256 0.004*

0.298 0.012*

0.142 0.043*

0.005* 0.065

0.006* 0.087*

0.007* 0.045*

0.012* 0.087*

0.345 0.192

0.005* 0.001*

0.013* 0.040*

0.672 0.300*

0.023* 0.020*

0.321 0.010*

0.002* 0.011*

0.034* 0.004*

0002* 0.002*

0.001* 0.606

0.003* 0.805

0.003* 0.706

0.231 0.542

Seasonality adjusted log returns H–J test D–P test

0.003* 0.023*

0.290 0.001*

Residuals from the bivariate VAR model H–J test D–P test

0.002* 0.001*

0.025* 0.002*

0.022* 0.034*

Residuals from the bivariate BEKK model H–J test D–P test

0.158 0.003

0.028* 0.026

0.003* 0.015

Residuals from the five-variate VAR model H–J test D–P test

0.876 0.181

0.003* 0.167

0.076* 0.571

0.654 0.045*

Residuals from the five-variate BEKK model H–J test D–P test

0.003* 0.002*

0.034* 0.128

0.076* 0.002*

0.004* 0.532

Note: Table presents p-values of the test statistics of D–P test—Diks and Panchenko test; H–J test—Hiemstra and jones test; VAR—vector autoregressions. *Significant at 5% level.

show that the news impact is asymmetric and significant for the TV, TVR, LIQ, and Hi–Low, since γ ̸ = 0. The values are negative and statistically significant for the TV and TVR implying that the negative shocks persist longer in the mean and conditional variance than the positive news. On the contrary, the findings show that the coefficients are positive and statistically significant for the LIQ and Hi–Low spread estimator. The impact of positive and negative news reveals that market liquidity is more aggravated through the positive and the negative shocks in the ASI.

Further, the presence of positive news does not support the leverage effect for the market liquidity variables. This evidence is consistent with the theoretical and empirical studies and confirm that high market liquidity is always more prone to sentiment shift through direct and indirect channels (bearish or bullish). Our findings show that an increase in the investor sentiment, which implies higher participation of noise traders increases the stock market liquidity. This evidence is consistent with the noise trader

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J. Kumari / Journal of Behavioral and Experimental Finance 23 (2019) 166–180

Table 8 Nonlinear causality statistics for ASI → LIQ and ASI → HiLow . Relation

ASI → LIQ

Lags lx = ly

1

2

ASI → HiLow

LIQ → ASI

HiLow → ASI

3

4

1

2

3

4

1

2

3

4

1

2

3

4

0.056* 0.001*

0.046* 0.003*

0.002* 0.005*

0.001* 0.021*

0.002* 0.023*

0.008* 0.023*

0.001* 0.022*

0.004* 0.001*

0.034* 0.005*

0.053* 0.086

0.065* 0.076

0.002* 0.087

0.003* 0.087

0.005* 0.087

0.000 0.000*

0.006* 0.006*

0.007* 0.000*

0.000* 0.000*

0.000* 0.002*

0.001* 0.036*

0.000* 0.017*

0.035* 0.004*

0.014* 0.005*

0.004* 0.004*

0.016* 0.003*

0.020* 0.001*

0.024* 0.000*

0.007* 0.005*

0.005* 0.006*

0.000* 0.007*

0.000* 0.006*

0.000* 0.000*

0.002* 0.000*

0.001* 0.000*

0.003* 0.000*

0.004* 0.000*

0.005* 0.006*

0.007* 0.007*

0.008* 0.008*

0.004* 0.005*

0.005* 0.009*

0.006* 0.005*

0.005* 0.000*

0.008* 0.000*

0.009* 0.000*

0.008* 0.000*

0.004* 0.000*

0.001* 0.000*

0.008* 0.003*

0.007* 0.001*

0.009* 0.002*

0.008* 0.003*

0.007* 0.006*

0.006* 0.000*

0.000* 0.000*

0.000* 0.002*

0.001* 0.006*

0.000* 0.007*

0.035* 0.004*

0.004* 0.005*

0.004* 0.004*

0.006* 0.003*

0.000* 0.001*

0.004* 0.000*

Seasonality adjusted log returns H–J test D–P test

0.003* 0.563

0.025* 0.678

Residuals from the bivariate VAR model H–J test D–P test

0.113* 0.014*

0.009* 0.000*

0.000* 0.001*

Residuals from the bivariate BEKK model H–J test D–P test

0.124 0.003*

0.009* 0.006*

0.008* 0.007*

Residuals from the five-variate VAR model H–J test D–P test

0.034* 0.004*

0.023* 0.009*

0.000* 0.007*

0.005* 0.008*

Residuals from the five-variate BEKK model H–J test D–P test

0.005* 0.004*

0.000* 0.000*

0.009* 0.001*

0.000* 0.000*

Note: Table presents p-values of the test statistics of D–P test—Diks and Panchenko test; H–J test—Hiemstra and jones test; VAR—vector autoregressions. *Significant at 5% level.

theory of De Long et al. (1990a,b). Overall, our empirical results are robust across different conditional variance models. 5.2. Nonlinear causality estimates The findings of the non-linear conditional GARCH class of models reveal that the market is liquid when ASI is higher. Nevertheless, the direction of the causality is not clear. It is always possible that the higher ASI increases the market liquidity because the bullish traders trade aggressively and create differences in the order flow of the market and price impact. On the other, the possibility of liquid market influencing sentiment cannot be ruled out. In other words, bidirectional causation is possible between liquidity and sentiment. Hence, I conduct the nonlinear Granger causality test to understand the direction of the causality. Nonlinear Granger causality between investor sentiment and liquidity is verified by employing the H–J and D–P tests in three sequential steps. First, the test was applied to the raw data, i.e. seasonally adjusted log returns. These findings show whether the causal relationships exist, but do not elucidate the nature of these relations. Therefore, in the second step, the tests are applied to the residuals drawn from the VAR models. In this condition, the rejection of the null hypothesis for such residuals implies causality is nonlinear and this filtering enables control of the linear interdependence between investor sentiment and the liquidity. Third, I further filter the residuals from the VAR models using the BEKK (1, 1) model and then employ the H–J and D–P tests on the standardized residuals from the BEKK models. In this way, I can examine if the detected nonlinear causality arises from the second-moment dependencies. Following Baek and Brock (1992), Hiemstra and Jones (1994) and Diks and Panchenko (2006) the H–J and D–P tests are applied on the standardized data. Four values of lags lx = ly = 1, 2, 3, 4 and a distance measure equal to 1.5 were considered in the analysis. The findings are presented in Tables 7 and 8. The null hypothesis of no causality is rejected for most of the seasonally adjusted variables except ASI → TV and TV → ASI. To understand the relationships are nonlinear, the residuals drawn from the VAR models need to be analyzed. The standardized residuals of the estimated bivariate VAR models confirm the nonlinear relationship for the following directions: ASI → TV , TV → ASIASI → TVR, ASI → LIQ , LIQ → ASI, ASI → HiLow and HiLow → ASI.

The findings for the standardized residuals from the BEKK model reveal that all of the nonlinearities arise from the secondmoment dependencies. I find bidirectional nonlinear causality between sentiment and liquidity measures. Further, the multivariate BEKK model reveals the causal relationship betweenASI → TV , TV → ASIASI → TVR, ASI → LIQ , LIQ → ASI, ASI → HiLow and HiLow → ASI. Therefore, unlike VAR models, the multivariate BEKK model reveals the bidirectional causation between the investor sentiment and the market liquidity in India. The findings, therefore, suggest a bidirectional nonlinear causality between investor sentiment and liquidity. The liquidity variables are significant for all selected lags. This implies that increased market liquidity influences investors to act as bullish with more trade executions in the markets and vice versa. In addition, investor sentiment also influences the market liquidity. Larger the noise traders exist in the markets, greater the irrational trading activities; such trading eventually affects the market liquidity through the indirect channel. In some cases, the H–J test rejects the hypothesis of no causality while the D–P test failed to do so because the former test tends to lead to spurious rejections of the null hypothesis. This suggests that the time lag between cause and effect is longer than the one lag. The findings suggest bidirectional causality between ASI and the market liquidity in India. The findings support the theoretical arguments that sentiment influences market liquidity through the direct channel (noise trading) and indirect channel (the irrational market makers). Further, bidirectional causality between the investor sentiment and LIQ and the Hi–Low implies that the institutional investors who dominate the Indian market often act as irrational risk arbitrageurs and drives the market away from fundamentals. Further, the market liquidity variation through the order flow, transaction activity, and price impact have equal significance to influence the ASI. Therefore, market liquidity remains one of the main components for the investors’ future decisions and investment strategies in non-synchronous markets such as India. I further corroborate that investor sentiment and the market liquidity exhibit bidirectional causality in markets such as India. 6. Conclusion I empirically investigated the theoretical interlinkages between the stock market liquidity and the investor sentiment in

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India. Unlike previous work on EMs, I constructed the aggregate investor sentiment index (ASI) for India. Departing from the existing literature, this study probed the time varying liquidity relationship with time varying investor sentiment in the nonlinear GARCH conditional framework. Further, I employed the nonlinear causality tests to understand the causal relationship between the investor sentiment and the stock market liquidity. The persistence in liquidity volatility, symmetric and asymmetric effects is evident from the GARCH class of models. Moreover, ASI acts as a time varying systematic risk factor and it needs to be priced into the market. Specifically, the findings suggest that ASI significantly influences the variation in market liquidity. Further, the findings from the nonlinear causality tests suggest the bidirectional relationship between liquidity and the investor sentiment. I conclude that the past psychological biases, overconfidence, optimism and herd behavior of investors are associated with the volatility of liquidity through direct and indirect channels. Unlike developed markets where retail investors are of the sizable number and their sentiment affects the stock market liquidity, our findings substantiate that institutional investor sentiment does induce the stock market liquidity and the volatility of liquidity in emerging economies such as India. The domestic and foreign investors can improve the volatility modeling of the stock market liquidity by incorporating the sentiment as a behavioral component apart from the macroeconomic and idiosyncratic factors. Acknowledgment I thank anonymous reviewer for the impactful comments and insightful suggestions. Usual disclaimer applies. References Aitken, B., 1998. Have institutional investors destabilized emerging markets? Contemp. Econ. Policy 16, 173–184. Alzahrani, M., Mansur, M., Al-Titi, O., 2014. Linear and non-linear granger causality between oil spot and futures prices: A wavelet-based test. J. Int. Money Financ. 48, 175–201. Amihud, Y., 2002. Illiquidity and stock returns: cross-section and time-series effects. J. Financ. Mark 5, 31–56. Baek, E., Brock, W., 1992. A general test for non-linear Granger causality: bivariate model. Working paper, Iowa State University and University of Wisconsin, Madison, WI. Baker, M., Stein, J.C., 2004. Market liquidity as a sentiment indicator. J. Financ. Mark 7 (3), 271–299. Baker, M., Wurgler, J., 2000. The equity share in new issues and aggregate stock returns. J. Financ. 55, 2219–2257. Baker, M., Wurgler, J., 2006. Investor sentiment and the cross-section of stock returns. J. Financ. 61 (4), 1645–1680. Baker, M., Wurgler, J., 2007. Investor sentiment in the stock market. J.Econ. Perspect. 21, 129–151. Baker, M., Wurgler, J., Yuan, Y., 2012. Global, local, and contagious investor sentiment. J. Financ. Econ. 104 (2), 272–287. Bampinas, G., Panagiotidis, T., 2015. On the relationship between oil and gold before and after financial crisis: linear, nonlinear and time-varying causality testing. Stud. Nonlinear Dyn. Econom. 19, 657–668. Barberis, N., Shleifer, A., 1998. Style investing. J. Financ. Econ. 68, 161–199. Barberis, N., Thaler, R., 2003. A survey of behavioral finance. In: Handbook of the Economics of Finance. pp. 1052–1121. Bekiros, S.D, 2014. Exchange rates and fundamentals: co-movement, long-run relationships and short-run dynamics. J. Bank. Financ. 39, 117–134. Black, F., 1986. Studies of stock price volatility changes. In: Proceedings of the Business and Economic Statistics. American Statistical Association, pp. 177–181. Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. J. Econom. 31, 307–327. Brennan, M.J., Chordia, T., Subrahmanyam, A., 1998. Alternative factor specifications, security characteristics, and the cross-section of expected stock returns. J. Financ. Econ. 49 (3), 345–373. Brown, G.W., 1999. Volatility. sentiment, and noise traders. J. of Financ. Analyst 55, 82–90.

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