The effect of investor sentiment on gold market return dynamics: Evidence from a nonparametric causality-in-quantiles approach

Resources Policy 51 (2017) 77–84

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The effect of investor sentiment on gold market return dynamics: Evidence from a nonparametric causality-in-quantiles approach☆ Mehmet Balcilara,b,c, Matteo Bonatod, Riza Demirere, Rangan Guptab,

⁎

a

Department of Economics, Eastern Mediterranean University, via Mersin 10, Famagusta, Northern Cyprus, Turkey Department of Economics, University of Pretoria, Pretoria 0002, South Africa IPAG Business School, Paris, France d Department of Economics and Econometrics, University of Johannesburg, Auckland Park, South Africa e Department of Economics & Finance, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1102, USA b c

A R T I C L E I N F O

A BS T RAC T

JEL codes: C22 Q02

This paper explores the effect of investor sentiment on the intraday return dynamics in the gold market. We build on the recent evidence by Da et al. (2015) that the Financial and Economic Attitudes Revealed by Search (FEARS) index, as a proxy for investor sentiment, has predictive power over stock market returns and extend the analysis to gold intraday returns using a novel methodology developed by Balcilar et al. (2016) to examine nonlinear casual effects of sentiment on gold return and volatility. We find that the effect of investor sentiment is more prevalent on intraday volatility in the gold market, rather than daily returns. The sentiment effect, however, is channeled via the discontinuous (jump) component of intraday volatility, particularly at extreme quantiles, implying that extreme fear (confidence) contributes to positive (negative) volatility jumps in gold returns. The results suggest that measures of sentiment could be utilized to model volatility jumps in safe haven assets that are often hard to predict and have significant implications for risk management as well as the pricing of options.

Keywords: Investor sentiment Gold returns Intraday volatility Volatility jumps

1. Introduction The relationship between investor sentiment and stock returns has been examined in numerous studies (see Huang et al., 2015 for a detailed literature review). Traditionally in empirical finance, two approaches have been followed to measure investor sentiment (Bathia and Bredin, 2013; Bathia et al., 2016). Under the first route, investor sentiment is captured by various market-based measures (e.g. trading volume, closed-end fund discount, initial public offering (IPO) first-day returns, IPO volume, option implied volatilities (VIX), or mutual fund flows) acting as proxies for investor sentiment, while survey based indices (University of Michigan Consumer Sentiment Index, the UBS/GALLUP Index for Investor Optimism, or investment newsletters) comprise the second approach. Recently, Da et al. (2015) develop a new measure of investor sentiment using daily Internet search data from millions of households in the U.S by focusing on particular ‘economic’ keywords that reflect investors’ sentiment towards economic developments. Their findings suggest that the so-called Financial and Economic Attitudes Revealed by Search (FEARS) index can predict short-term stock market rever-

sals, temporary increases in stock market volatility, and mutual fund outflows from equity to bond funds. Da et al. (2015) argue that this ‘search-based’ measure of investor sentiment reveals attitudes rather than inquire about them, and hence, provides a more accurate proxy for investor sentiment than survey-based measures that may be driven by answers in survey data that have not been cross-verified with data on actual behavior. Interestingly, among the economic keywords they focus on in their internet search data, Da et al. (2015) observe that the keyword “Gold prices” stands out from the other keywords with the highest level of statistical significance when the keywords are related to the market return. As argued in numerous studies, gold is traditionally considered to be a hedge or safe haven for financial market investors due to its low and sometimes negative correlation with financial market movements, particularly during bad times (e.g. Baur and Lucey, 2010). To that end, it is not unexpected to see ‘Gold returns’ as a dominant keyword that comes up in the search data that forms the basis for the investor sentiment index developed by Da et al. (2015). Therefore, the main motivation for this study is the natural research question whether the FEARS index as a proxy for investor sentiment has any explanatory

☆ ⁎

We would like to thank an anonymous referee for many helpful comments. Any remaining errors are solely ours. Corresponding author. E-mail addresses: [email protected] (M. Balcilar), [email protected] (M. Bonato), [email protected] (R. Demirer), [email protected] (R. Gupta).

http://dx.doi.org/10.1016/j.resourpol.2016.11.009 Received 1 May 2016; Received in revised form 6 November 2016; Accepted 18 November 2016 0301-4207/ © 2016 Elsevier Ltd. All rights reserved.

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quantiles show that causal effect of sentiment on volatility jumps is significant only at upper and lower quantiles, suggesting that extreme fear (confidence) contributes to positive (negative) volatility jumps in gold returns. These findings have significant implications for volatility forecasting and option pricing as they suggest that measures of investor sentiment can be utilized to predict volatility jumps that are often hard to predict due to their discontinuous nature. In the volatility forecasting context, the findings suggest that sentiment can be utilized to improve volatility jump models while other predictors can be targeted to model the permanent component of volatility. This means that investors and policy makers alike can track investor performance proxies in order to mitigate the negative effects of ‘bad jumps’ in volatility. Similarly, since volatility is a key parameter in option pricing models, the evidence presented in this paper can be used as basis for sentiment-based option pricing models in which sentiment proxy is integrated into the volatility parameter of the pricing model. Finally, given the evidence that volatility jump risk is priced in the cross-section of stock returns, sentiment proxies can be used as a systematic risk factor in asset pricing models and future studies can build on our evidence to examine whether sentiment uncertainty carries significant price of risk in stock returns. The rest of the paper is organized as follows: Section 2 presents the methodology and realized measures of gold market dynamics, while Section 3 discusses the data and the results. Finally Section 4 concludes.

power over gold market return dynamics. If investor sentiment can predict reversals and increases in volatility in the stock market as Da et al. (2015) document, one can argue that it should also possess similar predictive ability for gold returns as the widely accepted safe haven. Furthermore, it can also be argued that such predictive ability should present itself during periods of extreme fear, which can be captured best by a quantile-based approach. This paper has several contributions to the literature. First, we examine the causality effect of investor sentiment on gold return dynamics using a novel methodology to detect nonlinear causalities. A number of studies in the literature including Hammoudeh and Yuan (2008), Pukthuanthong and Roll (2011), Reboredo (2013), Beckmann and Czudaj (2013), and Pierdzioch et al. (2014), have used predictive regressions and GARCH-type models to examine the predictive value of various economic and financial variables like stock market returns, exchange-rate movements, oil-price fluctuations, and interest rates over gold market returns. The novel feature of this study is that it employs the causality-in-quantiles test, recently developed by Balcilar et al. (2016), and examine causality effects of sentiment during alternative market states that can be characterized by normal, good and bad markets. To the best of our knowledge, such a quantile-based analysis of causality between investor sentiment and gold return dynamics is the first in the literature. It must be noted that, other nonlinear causality tests (e.g. Nishiyama et al., 2011) and GARCH-type models could also be used to analyze the impact of investor sentiment on gold returns and/or volatility, but these methods rely on estimations based on the conditional means, and hence fail to capture the entire conditional distribution of gold returns and volatility – something we can do with our approach. In the process, our test is a more general procedure of detecting causality in both returns and volatility simultaneously at each point of the respective conditional distributions. Hence, we are able to capture existence or non-existence of causality at various market states (bear, i.e. lower quantiles, normal, i.e. median and bull, i.e. upper quantiles) for the gold market. Therefore, our method is more likely to pick up causality when conditional mean-based tests might fail to do so. Furthermore, since the procedure does not require the determination of the number of regimes as in a Markov-switching model and can test causality at each point of the conditional distribution characterizing specific regimes, our test also does not suffer from any misspecification in terms of specifying and testing for the optimal the number of regimes. Another important contribution of this study is that it provides novel insight to the effect of sentiment on market volatility by breaking intraday volatility in the gold market into continuous and discontinuous (i.e. jump) components. Volatility jumps have been well-documented in financial returns (e.g. Barndorff-Nielsen and Shephard, 2004) and several studies have also shown that jump risk can serve as a systematic risk factor in stock returns (e.g. Dunham and Friesen, 2007). To that end, this study examines volatility jumps in novel context and by relating volatility jumps to investor sentiment during various market states, enlarges our understanding of the evidence by Da et al. (2015) that sentiment predicts temporary increases in volatility. Looking ahead, while we observe no significant causal effects of sentiment on daily gold returns, we find strong evidence of causality on intraday volatility in gold returns. The evidence of causality on intraday volatility is significant across all quantiles of the conditional distribution of intraday volatility. Interestingly, however, we also find that the sentiment effect on gold market volatility is channeled via not the permanent component of return volatility, but rather the discontinuous (jump) component, suggesting that sentiment contributes to volatility jumps in gold returns. This is in fact consistent with the earlier finding by Da et al. (2015) that sentiment predicts temporary increases in stock market volatility, possibly indicating that sentiment contributes to volatility jumps in stock returns as well. Finally, our tests at different

2. Methodology 2.1. Detecting nonlinear causality We present here a novel methodology, recently proposed by Balcilar et al., (2016), for the detection of nonlinear causality. The causality-inquantile approach combines the frameworks of k-th order nonparametric causality of Nishiyama et al. (2011) and nonparametric quantile causality of Jeong et al. (2012), and unlike the standard causality tests, has the following advantages: First, it is robust to misspecification errors as it detects the underlying dependence structure between the examined time series. Second, via this methodology, we are able to test for not only causality-in-mean (1st moment), but also causality that may exist in the tails of the joint distribution of the variables. Finally, we are also able to investigate causality-in-variance, thereby effect on volatility, as it is possible to have higher order interdependencies even when causality in the conditional-mean is not present. We denote returns on gold futures as (yt ) and the investor sentiment index as (xt ). Following Jeong et al., (2012), the quantile-based causality is defined as follows1: xt does not cause yt in the θ -quantile with respect to the lag-vector of {yt −1, …, yt − p , xt −1, …, xt − p} if

Qθ (yt yt −1, …,

yt − p , xt −1, …, xt − p )=Qθ (yt yt −1, …,

yt − p )

(1)

xt is a prima facie cause of yt in the θ -th quantile with respect to {yt −1, …, yt − p , xt −1, …, xt − p} if Qθ (yt yt −1, …,

yt − p , xt −1, …, xt − p )≠Qθ (yt yt −1, …,

yt − p )

(2)

where Qθ (yt ∙) is the θ -th quantile of yt depending on t and 0 < θ < 1. Xt −1≡(xt −1, …, xt − p ), Z t =(Xt , Yt ), and Let Yt −1≡(yt −1, …, yt − p ), Fyt | Zt−1 (yt | Z t −1) and Fyt | Yt−1 (yt | Yt −1) denote the conditional distribution functions of yt given Z t−1 and Yt−1, respectively. The conditional distribution Fyt | Zt−1 (yt | Z t −1) is assumed to be absolutely continuous in yt for almost all Z t−1. If we denote Qθ (Z t −1) ≡ Qθ (yt |Zt −1) and Qθ (Yt −1) ≡ Qθ (yt |Yt −1), we have Fyt | Zt−1 {Qθ (Z t −1) | Z t −1}=θ with probability one. Consequently, the hypotheses to be tested based on definitions 1 The exposition in this section closely follows Nishiyama et al. (2011) and Jeong et al. (2012).

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order moments using the following model:

(1) and (2) are:

H0 : P {Fyt | Zt−1 {Qθ (Yt −1) | Z t −1}=θ}=1

(3)

H1 : P {Fyt | Zt−1 {Qθ (Yt −1) | Z t −1}=θ} <1

(4)

yt =g (Xt −1, Yt −1)+εt Thus, higher order quantile causality can be specified as:

Jeong et al. (2012) employs the distance measure J = {εt E (εt | Z t −1) fZ (Z t −1)} where εt is the regression error term and fZ (Z t−1) is the marginal density function of Z t−1. The regression error εt emerges based on the null in (3), which can only be true if and only if E [1 {yt ≤Qθ (Yt −1) Z t −1}]=θ or equivalently 1 {yt ≤Qθ (Yt −1)}=θ + εt , where 1{∙} is an indicator function. Jeong et al. (2012) specify the distance measure as follows:

J =E [{Fyt | Zt−1 {Qθ (Yt −1) | Z t −1} − θ}2 fZ (Z t −1)]

1 T (T −1) h2p

T

T

∑

∑

t = p +1 s = p +1,

s≠t

⎛ Z − Zs −1 ⎞ K ⎜ t −1 ⎟ εˆt εˆs ⎠ ⎝ h

(5)

(6)

where K (⋅) is the kernel function with bandwidth h , T is the sample size, p is the lag-order, and εˆt is the estimate of the unknown regression error, which is estimated as follows:

εˆt =1{yt ≤Qˆ θ (Yt−1)} − θ

(7)

Qˆ θ (Yt−1) is an estimate of the θ -th conditional quantile of yt given Yt−1. Below, we estimate Qˆ θ (Yt−1) using the nonparametric kernel method as: −1 Qˆ θ (Yt −1)=Fˆyt | Yt−1 (θYt −1)

(8)

where Fˆyt | Yt−1 (yt Yt −1) is the Nadarya-Watson kernel estimator given by: T

Fˆyt | Yt −1 (yt Yt −1)=

Yt −1 − Ys −1 ) 1 (ys ≤ yt ) h T Y −Y ∑s = p +1, s ≠ t L ( t −1 h s −1 )

∑s = p +1, s ≠ t L (

(9)

with L (∙) denoting the kernel function and h the bandwidth. In an extension of the Jeong et al. (2012) framework, we develop a test for the 2nd moment. In particular, we want to test the volatility causality running from the investor sentiment index to volatility of gold returns. Causality in the k -th moment generally implies causality in the m -th moment for k < m . Firstly, we employ the nonparametric Granger quantile causality approach by Nishiyama et al. (2011). In order to illustrate the causality in higher order moments, consider the following process for yt :

yt =g (Yt −1)+σ (Xt −1) εt

⎫ ⎧ H1 : P ⎨F yt2 | Zt −1 {Qθ (Yt −1) | Z t −1}=θ ⎬ <1 ⎭ ⎩

(12)

⎧ ⎫ H1 : P ⎨F ytk | Zt−1 {Qθ (Yt −1) | Z t −1}=θ ⎬ <1fork =1, 2, …, K ⎩ ⎭

(15)

An advantage of using intraday data is that we are also able to compute measures of realized volatility which allows us to check the robustness of our findings across different volatility estimators. Below, we provide the details for the realized measures considered in the analysis. 2.2.1. Realized volatility estimator The first measure we consider is the classical estimator of realized volatility, i.e. the sum of squared intraday returns (Andersen and Bollerslev, 1998), expressed as

where εt is a white noise process; and g (∙) and σ (∙) are unknown functions that satisfy certain conditions for stationarity. However, this specification does not allow for Granger-type causality testing from Xt−1 to yt , but could possibly detect the “predictive power” from Xt−1 to yt2 when σ (∙) is a general nonlinear function. Hence, the Granger causality-in-variance definition does not require an explicit specification of squares for Xt−1. We re-formulate Eq. (10) into a null and alternative hypothesis for causality in variance as follows:

(11)

(14)

2.2. Measure of gold return dynamics

(10)

⎧ ⎫ H0 : P ⎨F yt2 | Zt −1 {Qθ (Yt −1) | Z t −1}=θ ⎬=1 ⎩ ⎭

⎧ ⎫ H0 : P ⎨F ytk | Zt−1 {Qθ (Yt −1) | Z t −1}=θ ⎬=1fork =1, 2, …, K ⎩ ⎭

Integrating the entire framework, we define that xt Granger causesyt in quantileθ up toK -th moment utilizing Eq. (14) to construct the test statistic of Eq. (6) for each k . However, it can be shown that it is not easy to combine the different statistics for each k = 1,2, …, K into one statistic for the joint null in Eq. (14) because the statistics are mutually correlated (Nishiyama et al., 2011). To efficiently address this issue, we include a sequential-testing method as described Nishiyama et al. (2011) with some modifications. Firstly we test for the nonparametric Granger causality in the 1st moment (k = 1). Rejecting the null of noncausality means that we can stop and interpret this result as a strong indication of possible Granger quantile causality-in-variance. Nevertheless, failure to reject the null for k = 1, does not automatically leads to no-causality in the 2nd moment, thus we can still construct the tests for k = 2 . Finally, we can test the existence of causality-invariance, or the causality-in-mean and variance successively. The empirical implementation of causality testing via quantiles entails specifying three important choices: the bandwidth h , the lag order p , and the kernel type for K (∙) and L (∙) in Eqs. (6) and (9), respectively. In our study, a lag order of 1 is used based on the Schwarz Information Criterion (SIC) under a VAR comprising of gold returns and the investor sentiment index. The SIC being parsimonious when it comes to choosing lags compared to other alternative lag-length selection criterion, helps us to prevent issues of overparametrization commonly associated with nonparametric approaches. The bandwidth value is selected using the least squares cross-validation method. Lastly, for K (∙) and L (∙) we employ Gaussian-type kernels.

In Eq. (3), it is important to note that J ≥ 0 , i.e., the equality holds if and only if H0 in (5) is true, while J > 0 holds under the alternative H1 in Eq. (4). Jeong et al. (2012) show that the feasible kernel-based sample analog of J has the following form:

JˆT =

(13)

M

RVt =

∑ rt2,i

(16)

i =1

where rt , i is the intraday M × 1 return vector and i = 1, …, M the number of intraday returns. 2.2.2. Realized Kernel estimator A second measure, which is robust to market microstructure noise and asynchronous, trading, is the realized Kernel estimator of Barndorff-Nielsen et al. (2008)expressed as H

To obtain a feasible test statistic for testing the null in Eq. (10), we replace yt in Eqs. (6)–(9) with yt2 . Incorporating the Jeong et al. (2012) approach we overcome the problem that causality in the conditional 1st moment (mean) imply causality in the 2nd moment (variance). In order to overcome this problem, we interpret the causality in higher

K (X )=

∑ h =− H

⎛ h ⎞ k⎜ ⎟γ , ⎝ H +1 ⎠ h

M

γh=

∑ j = h +1

xj xj −| h | (17)

where k (x ) is a kernel weight function and xj is the j-th high frequency return with j ∈ 1, …, M . 79

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gold on dayt .

2.2.3. Volatility jump estimator A number of studies including Barndorff-Nielsen and Shephard (2004), Huang and Tauchen (2005), Andersen et al. (2007) have documented the presence of volatility jumps in higher frequency time series. Studies including Dunham and Friesen (2007) and Zhou and Zhu (2012) further show that jump risk accounts for a significant percentage of variation in total return volatility and that it can also serve as a systematic risk factor in the cross-section of returns. Barndorff-Nielsen and Shephard (2004) show that realized volatility converges into permanent and discontinuous (jump) components as

M →∞

3.1. Data Gold futures data is in continuous format. Close to expiration of a contract, the position is rolled over to the next available contract, provided that activity has increased. Our dataset spans the period 1st July, 2004 to 24th March, 2011 using 1-min frequency data. The minute frequency is constructed using the last price that occurs in the 1-min interval.2 Gold futures are traded in NYMEX over a 24-h trading day (pit and electronic). Investor sentiment is measured by the Financial and Economic Attitudes Revealed by Search (FEARS) index recently developed by Da et al. (2015). This index utilizes daily Internet search data from a large number of households in the U.S. with a focus on particular sentimentrevealing keywords such as ‘recession’ or ‘unemployment’ and proxies the level of the sentiment of American households by aggregating the search data across economy-related keywords.3 After the removal of obvious holidays, days with limited market hours (e.g. December 24), and matching the data with the investor sentiment index, we are left with 1696 observations. Table 1 presents the summary statistics for daily gold returns and the FEARS index as a proxy for investor sentiment. Both variables are non-normal as suggested by the strong rejection of the null of normality under the Jarque-Bera statistic. Examining the skewness and kurtosis values, we see that non-normality of the two series arises due to gold returns being skewed to the left and the investor sentiment to the right, and the fact that both the series display excess kurtosis. The evidence suggesting the presence of heavy tails provides an initial motivation to look at quantiles rather than a conditional mean based approach. Fig. 1 plots the data involving the two variables of concern, i.e., gold returns and the FEARS index.

Nt

t

lim RVt =

3. Data and empirical findings

∫t−1 σ 2 (s) ds+ ∑ kt2,j,

(18)

j =1

where Nt is the number of jumps within day t and kt , j is the jump size. This specification suggests that RVt is a consistent estimator of the t integrated variance ∫ σ 2 (s ) ds plus the jump contribution. The t −1 asymptotic results of Barndorff-Nielsen and Shephard (2004, 2006) further show that t

lim BVt =

M →∞

∫t−1 σ 2 (s) ds

(19)

where BVt is the realized bipolar variation defined as

⎛ N ⎞ BVt =μ1−1 ⎜ ⎟ ⎝ M −1 ⎠

M

∑

rt , i −1 ri, t =

i =2

π 2

M

∑

rt , i −1 ri, t

(20)

i =2

and

μa =E (|Z |a ),

Z ~N (0, 1),

a>0.

(21)

Having defined the continuous component of realized volatility, a consistent estimator of the pure jump contribution can then be expressed as (22)

Jt =RVt −BVt

In order to test the significance of the jumps, we adopt the following formal test estimator proposed by Barndorff-Nielsen and Shephard (2006)

JTt =

3.2. Empirical fndings

RVt − BVt 1

(vbb − vqq ) N QPt

While the evidence of non-normality in the distribution of gold returns and the investor sentiment index provides the motivation for a quantile-based analysis, we perform additional tests in order to further justify the adoption of a nonlinear or nonparametric approach. More specifically, we perform the test of nonlinearity by Brock et al. (1996, BDS) and tests of multiple structural breaks by Bai and Perron (2003). The BDS test is applied on the residuals obtained from the model for gold returns estimated with a constant, a lag of its own and the lag of the investor sentiment index. Examining the results presented in Table 2, the null of i.i.d. residuals at various embedding dimensions (m) is rejected strongly at the highest level of significance, providing strong evidence of nonlinearity in the relationship between gold returns and the investor sentiment index. Understandably, a linear framework to test for causality would be misspecified. For this reason, we next turn to the Bai and Perron (2003) test of multiple structural breaks, applied again to the equation for gold returns estimated with a constant, a lag of its own and the lag of the investor sentiment index. Based on the powerful WDMax test, we detect three break dates: 16th December, 2005; 18th May, 2006; and 21st September, 2006.4 As a result, as with the BDS test which detects nonlinearity, the evidence of structural breaks in the relationship between gold returns and investor sentiment implies that the standard Granger causality test based on a linear framework is likely to suffer

(23)

where QPt is the Tri-Power Quarticity defined as

⎛ M ⎞ TPt =M μ −3 ⎜ ⎟ 4/3 ⎝ M −1 ⎠

M

∑ |rt,i −2 |4/3 |rt,i |4/3

(24)

i =3

which converges to t

TPt →

∫t−1 σ 4 (s) ds

(25) π vbb=( 2 )2 +π −3

and vqq=2. Note that for even in the presence of jumps. each t,JTt ~N (0, 1) asM→∞. As can be seen in Eq. (22), the jump contribution to RVt is either positive or null. Therefore, in order to avoid having negative empirical contributions, we follow Zhou and Zhu (2012) and re-define the jump measure as (26)

RJt =max (RVt −BVt ; 0)

In a recent study, Guo et al. (2015) document the asymmetric forecasting power of positive and negative jumps on the conditional equity premium using U.S. market data. In order to capture possible asymmetric effects due to positive and negative jumps, we further decompose the total realized jump measure (RJ) into a component for negative and a component for positive jumps and construct a signed realized jump measure (RJS) measure expressed as

RJSt =RJt+−RJt− where

RJt+=RJt 1r gold ≥0 , t

2

Data is provided by www.disktrading.com. The data is available for download from: http://www3.nd.edu/~zda/fears_post_ 20140512.csv. 4 If we use the F-statistics, we see that there are as many as nine breaks in the relationship between gold returns and the FEARS index. 3

(27)

RJt−=RJt 1r gold ≤0 t

and

rtgold

is the return on the 80

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Table 1 Summary statistics.

Table 3 Quantile slope equality test.

Statistic

Gold return

Fears

Mean Median Maximum Minimum Std. dev. Skewness Kurtosis Jarque-Bera Probability Observations

0.0007 0.0012 0.0947 −0.0797 0.0126 −0.3955 8.3208 2044.8810 0.0000 1696

0.0016 −0.0161 3.1864 −2.5498 0.3580 1.8191 21.1398 24,188.4900 0.0000 1696

Estimated equation quantile tau=0.5 User-specified test quantiles: 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9 Test statistic compares all coefficients Test summary Chi-Sq. Statistic Chi-Sq. d.f. Prob. Wald test 56.9795 32 0.0042 Note: This table presents the results for the Koenker and Bassett (1982) test of slope homogeneity. The null hypothesis is the equality of slopes in the equation for gold returns regressed against a constant, lagged gold return and the lagged FEARS index, across various quantiles ranging between 0.1 and 0.9.

vindicating the use of the nonparametric causality-in-quantiles method over the linear test of causality. Fig. 2 presents the results of the non-parametric causality-inquantiles tests when we regress gold market related variables against the FEARS index. As explained earlier, we examine a number of volatility estimators using intraday return data for gold in addition to daily gold returns. Interestingly, our tests do not yield any causal effects of sentiment on daily gold returns, consistently across all conditional quantiles of the empirical distribution. However, we observe strong evidence of causality from sentiment to gold volatility, consistently across the different volatility estimators considered. Furthermore, the evidence of causality is strong across all quantiles of the conditional distribution of gold return volatility, suggesting that investor sentiment mainly contributes to volatility in safe haven markets, potentially hurting the effectiveness of hedging strategies in these markets. Coupled with the evidence in Da et al. (2015) that sentiment has predictive power over stock market volatility, one can also argue that volatility interactions across the stock and gold markets are primarily affected by changes in investor sentiment.5

Note: Std. Dev. stands for standard deviation, and Probability corresponds to the null hypothesis of non-normality of the Jarque-Bera test.

3.2.1. Components of realized volatility As mentioned earlier, Da et al. (2015) report that investor sentiment can predict temporary increases in stock market volatility. In fact, a number of studies in the literature suggest that volatility jumps can explain a significant percentage of the total variation in return variability in the stock market. To that end, a natural question is whether the documented sentiment effect on gold market volatility presents itself in the permanent or jump component (or both) of intraday volatility. If in fact, the sentiment effect is limited to the permanent component of volatility, then one can argue that the effect is possibly an artifact of the volume-volatility relationship in which volatility is driven by trading activity, as argued by Giot et al. (2010). However, if the sentiment effect is limited to the jump component, it will have significant investment and modeling implications as volatility jumps are shown to be significant in a number of different contexts. In order to provide further insight to the sentiment effect on volatility, we decompose realized volatility (RV) in Eq. (16) into permanent (BV) and jump (RJ) components as shown in Eqs. (20) and (26), respectively. Next, motivated by Guo et al. (2015), we further differentiate between positive and negative jumps as shown in Eq. (27) and perform causality tests on the signed realized jump measure (RJS). This differentiation allows us to examine possible asymmetries in the causal effects of sentiment on volatility. Fig. 3 presents the results of

Fig. 1. Timer series plots. Table 2 BDS test of nonlinearity. m

BDS statistic

Std. error

z-statistic

p-value

2 3 4 5 6

0.0103 0.0257 0.0363 0.0431 0.0471

0.0021 0.0033 0.0039 0.0041 0.0040

4.9794 7.7875 9.2367 10.5177 11.9023

0.0000 0.0000 0.0000 0.0000 0.0000

Note: This table presents the results for the test of nonlinearity by Brock et al. (1996, BDS). m stands for the number of (embedded) dimensions which embed the time series into m-dimensional vectors, by taking each m successive points in the series. Values in the fourth column represent BDS z-statistic corresponding to the null of i.i.d. residuals.

5 Based on the suggestion of an anonymous referee, we also estimated models of the GARCH family with the lagged investor sentiment affecting both returns and volatility. We observed that the investor sentiment failed to cause returns, but had significant causal impact on volatility, hence, corroborating the evidence for our causality-inquantiles approach. But since the causality-in-quantiles approach helps us to study the entire conditional distribution of returns and volatility, rather than just the conditional mean as in the GARCH models, and given the evidence of breaks and nonlinearities in the relationship between gold returns and the sentiment index, we prefer our nonparametric approach over the GARCH-based method. Complete details of these results are available upon request from the authors.

from misspecification. Given the strong evidence of both nonlinearity and regime changes, we now turn to the causality-in-quantiles test. As a final test of the suitability of this framework, we also conduct the Koenker and Bassett (1982) test of slope homogeneity, and, as shown in Table 3, the null of equality of slopes across the various quantiles for the gold returns equation regressed against a constant and lagged gold returns and the FEARS index is overwhelmingly rejected; thus 81

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Fig. 2. Quantile causality from sentiment to gold return and volatility. Note: The figure presents the results of the causality-in-quantiles tests from sentiment to gold return, squared return, Realized Volatility (RV), Realized Kernel (RVK) and the Two-Time Scale (RVTS) estimators. The solid dark line represents the 5% confidence level.

Fig. 3. Quantile causality from sentiment to components of realized volatility. Note: The figure presents the results of the causality-in-quantiles tests from Sentiment to the permanent (BV), discontinuous, i.e. jump, (RJ) components of realized volatility as well as the signed jump measure (RJS). The solid dark line represents the 5% confidence level.

only, implied by insignificant causality results for the permanent component (BV). Following the evidence in Giot et al. (2010), this finding implies that the sentiment effect on volatility is not necessarily an artifact of the volume-volatility relationship in the gold market.

the causality-in-quantiles tests when we regress the permanent, jump and signed jump measures against the FEARS index. Interestingly, the tests on the different components of realized volatility show that the sentiment effect on volatility is channeled via the jump component

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systematic risk factor in asset pricing models and future studies can build on our evidence to examine whether sentiment uncertainty carries significant price of risk in stock returns.

On the other hand, turning our focus on the jump component of realized volatility, we see that the effect of sentiment is significant around the median of the conditional distribution of the realized jump values. We get further insight to this observation when we differentiate between positive and negative jumps and examine the signed realized jump measure (RJS) in Fig. 3. The results for the signed jump measure show that the sentiment effect on volatility jumps is in fact present only in the upper and lower quantiles, implied by the u-shaped pattern in the plot for this component of volatility. This finding suggests that the causal effect of sentiment is particularly strong during periods of extreme fear and confidence captured by the extreme quantiles, implying that extreme fear (confidence) contributes to positive (negative) volatility jumps in gold returns. The finding that extreme fear, implied by high values for the FEARS index, contributes to positive volatility jumps is consistent with the safe haven literature (e.g. Baur and Lucey, 2010; Hood and Malik, 2013; Agyei-Ampomah et al., 2014) in that it reflects investors’ tendency to flock to gold during periods of high market stress. It is also consistent with the finding by Da et al. (2015) that sentiment predicts temporary increases (jumps) in stock market volatility, indicating that sentiment contributes to volatility jumps in stock market volatility as well. To that end, our findings provide new insight to Da et al. (2015) regarding the channel through which sentiment impacts market volatility. The findings also have economic implications as they relate particularly to volatility forecasting and the pricing of derivatives. The finding that high level of fear contributes to positive volatility jumps in the gold market can be good news for volatility forecasting purposes as it suggests that sentiment can potentially be used to improve models of volatility jumps that are often hard to predict due to their discontinuous nature. This is especially important for traders in the gold volatility index (VIX) futures as investors can utilize investor sentiment to devise trading rules based on the predictive ability of sentiment for gold market volatility. The sentiment effect can also be used in short-term market timing strategies in which investors divert funds across the risky and safe haven assets based on the direction of investor sentiment. In the volatility forecasting context, the findings suggest that sentiment can be utilized to improve volatility jump models while other predictors can be targeted to model the permanent component of volatility. Considering the insignificant findings reported for the permanent component of volatility, a dual-forecasting model can be utilized in which trading based variables are used to forecast the permanent component and sentiment proxies are used to forecast the jump component of volatility. This is in fact an important issue for policy makers who are concerned about the stability in the financial markets. If ‘bad jumps’ in volatility can be predicted by sentiment proxies, as the results indicate, this information can be utilized towards modeling and monitoring volatility shocks in financial markets and consequently, courses of action to effectively cushion the impact of volatility shocks could be designed. The predictive value of sentiment on volatility jumps in gold also has implications for the pricing of gold options and futures as volatility jumps can significantly affect the pricing of derivative securities. Since volatility is a key parameter in option pricing models, the evidence presented in this paper can be used as basis for sentiment-based option pricing models in which sentiment proxy is integrated into the volatility parameter of the pricing model. Significant causality observed on the lower quantile of the conditional distribution of RJS values reported in Fig. 3 suggests that extreme investor confidence can impact volatility jumps in gold, however, in the negative direction. This finding is interesting in that extreme investor confidence can potentially contribute to crashes in commodities that are considered to be safe haven assets. To that end, it would be interesting to see if sentiment has a significant effect in the risk premium embedded in gold derivatives prices. Finally, given the evidence that volatility jump risk is priced in the cross-section of stock returns, sentiment proxies can be used as a

4. Conclusion This paper contributes to the literature on investor sentiment and financial market dynamics by examining the effect of investor sentiment on gold return and volatility using a novel methodology to detect nonlinear causalities. Our findings suggest that sentiment effect is more prevalent on the intraday volatility, rather than daily returns, in the gold market. Interestingly, however, the sentiment effect on gold market volatility is channeled via not the permanent component of realized volatility, but rather the jump component, suggesting that sentiment contributes to volatility jumps in gold returns. This finding provides new insight to the sentiment-stock market volatility relationship as the investor sentiment effect documented in the literature can be largely driven by its contribution to jump risk in the stock market. Examining the test results for alternative quantiles of the conditional distribution of sentiment and volatility, we find that the causal effect of sentiment on volatility jumps is significant only at upper and lower quantiles, suggesting that extreme fear (confidence) contributes to positive (negative) volatility jumps in gold returns. While it is not unexpected to find that extreme market stress drives positive volatility jumps in a safe haven asset like gold, it is also interesting that extreme confidence causes negative volatility jumps in the gold market, possibly contributing to crashes. Nevertheless, the findings have significant economic and policy making implications as they suggest that measures of investor sentiment can be utilized to predict volatility jumps that are often hard to predict due to their discontinuous nature. References Agyei-Ampomah, S., Gounopoulos, D., Mazouz, K., 2014. Does gold offer a better protection against losses in sovereign debt bonds than other metals? J. Bank. Financ. 40, 507–521. Andersen, T.G., Bollerslev, T., 1998. Answering the skeptics: yes, standard volatility models do provide accurate forecasts. Int. Econ. Rev. 39 (4), 885–905. Andersen, T.G., Bollerslev, T., Diebold, F.X., 2007. Roughing it up: including jump components in the measurement, modeling, and forecasting of return volatility. Rev. Econ. Stat. 89 (4), 701–720. Bai, J., Perron, P., 2003. Computation and analysis of multiple structural change models. J. Appl. Econ. 18, 1–22. Balcilar, M., Bekiros, S., Gupta, R., 2016. The role of news-based uncertainty indices in predicting oil markets: a hybrid nonparametric quantile causality method. Empir. Econ.. http://dx.doi.org/10.1007/s00181-016-1150-0. Barndorff-Nielsen, O.E., Shephard, N., 2004. Power and bipower variation with stochastic volatility and jumps. J. Financ. Econ. 2, 1–37. Barndorff-Nielsen, O.E., Shephard, N., 2006. Econometrics of testing for jumps in financial economics using bipower variation. J. Financ. Econ. 4, 1–30. Barndorff-Nielsen, O.E., Hansen, P.R., Lunde, A., Shephard, N., 2008. Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise. Econometrica 76, 1481–1536. Bathia, D., Bredin, D., 2013. An examination of investor sentiment effect in G7 stock market returns. Euro. J. Financ. 19 (9), 909–937. Bathia, D., Bredin, D., Nitzsche, D., 2016. International sentiment spillovers in equity returns. Int. J. Financ. Econ. 21 (4), 332–359. Baur, D.G., Lucey, B.M., 2010. Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financ. Rev. 45, 217–229. Beckmann, J., Czudaj, R., 2013. Oil and gold price dynamics in a multivariate cointegration framework. Int. Econ. Econ. Policy 10, 453–468. Brock, W., Dechert, D., Scheinkman, J., LeBaron, B., 1996. A test for independence based on the correlation dimension. Econom. Rev. 15, 197–235. Da, Z., Engelberg, J., Gao, P., 2015. The sum of all fears investor sentiment and asset prices. Rev. Financ. Stud. 28 (1), 1–32. Dunham, L.M., Friesen, G.C., 2007. An empirical examination of jump risk in U.S. equity and bond markets. N. Am. Actuar. J. 11 (4), 76–91. Giot, P., Laurent, S., Petitjean, M., 2010. Trading activity, realized volatility and jumps. J. Empir. Financ. 17 (1), 168–175. Guo, H., Wang, K., Zhou, H., 2015. Good Jumps, Bad Jumps, and Conditional Equity Premium. Working Paper (February 2015). University of Cincinnati. Hammoudeh, S., Yuan, Y., 2008. Metal volatility in presence of oil and interest rate shocks. Energy Econ. 30, 606–620. Hood, M., Malik, F., 2013. Is gold the best hedge and a safe haven under changing stock market volatility? Rev. Financ. Econ. 22, 47–52.

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Huang, D., Jiang, F., Tu, J., Zhou, G., 2015. Investor sentiment aligned: a powerful predictor of stock returns. Rev. Financ. Stud. 28, 791–837. Jeong, K., Härdle, W.K., Song, S., 2012. A consistent nonparametric test for causality in quantile. Econom. Theory 28, 861–887. Koenker, R.W., Bassett, G.S., Jr., 1982. Robust tests for heteroscedasticity based on regression quantiles. Econometrica 50, 43–61. Nishiyama, Y., Hitomi, K., Kawasaki, Y., Jeong, K., 2011. A consistent nonparametric test for nonlinear causality - specification in time series regression. J. Econ. 165, 112–127.

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