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Time variation in systematic risk, returns and trading volume: Evidence from precious metals mining stocks
Time Variation in Systematic Risk, Returns and Trading Volume: Evidence from Precious Metals Mining Stocks Cetin Ciner PII: DOI: Reference:
S1057-5219(15)00030-7 doi: 10.1016/j.irfa.2015.01.019 FINANA 809
To appear in:
International Review of Financial Analysis
Please cite this article as: Ciner, C., Time Variation in Systematic Risk, Returns and Trading Volume: Evidence from Precious Metals Mining Stocks, International Review of Financial Analysis (2015), doi: 10.1016/j.irfa.2015.01.019
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ACCEPTED MANUSCRIPT Time Variation in Systematic Risk, Returns and Trading Volume:
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Evidence from Precious Metals Mining Stocks
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Cetin Ciner Professor Finance Department of Economics and Finance Cameron School of Business University of North Carolina Wilmington E-mail: [email protected]
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January 17, 2015
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Abstract: We investigate whether trading volume has explanatory power for time variation in CAPM betas as well as returns, for the precious metals mining sector. We show that significant dependencies exist between these variables; however, empirical linkages are only revealed when quantile regression method is employed. The observed dynamics are particularly strong between trading volume and returns. We find that returns from lower (higher) quantiles have a negative (positive) relation with volume. We discuss the consistency of this asymmetric relation with equilibrium volume-return autocorrelation models suggested in prior work. JEL Classification: G0, G15 Keywords: trading volume, quantile regression, returns, beta
I am grateful to comments by two referees, which significantly improved this study. All remaining errors are my responsibility. Time Variation in Systematic Risk, Returns and Trading Volume: Evidence from Gold Mining Stocks 1. Introduction
ACCEPTED MANUSCRIPT Beta, as the sole measure of systematic risk according to the Capital Asset Pricing Model (CAPM), occupies a central role in modern finance theory. Financial researchers as well as
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market practitioners rely on the beta coefficient to correctly value stocks, to calculate the cost of capital of a corporation and also, to evaluate the performance of portfolio managers. In the
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context of the CAPM, beta is assumed to be constant over time and therefore, can be easily estimated. However, financial researchers, beginning by the early work by Sharpe et al. (1974),
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and Fabozzi and Francis (1978), have consistently argued that observed betas are not constant,
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rather they exhibit significant variation through time.
Subsequent research in this area has largely focused on the impact of macroeconomic
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variables, such as industrial production and inflation, to explain the time variation in betas.
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Recent examples of this strand of the literature include Mergner and Bulla (2008), Andersen et al. (2005) and Lettau and Ludvingson (2001) among others. Unfortunately, a common
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conclusion of these articles is that macroeconomic variables have little explanatory power for
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understanding the time variation in individual stock betas. In this paper, we further investigate the time variation in betas by adopting a view towards microeconomic, rather than macroeconomic, factors. As a novel addition to the literature, we examine whether trading volume can explain the observed time variation in systematic risk of stocks in the precious metals mining sector. Our hypothesis that trading volume can explain time-variation in CAPM betas stems from market microstructure models, such as the well-known mixture of distributions hypothesis, which assign a special importance to trading volume, as a proxy for the rate of information flow to the market. Also, Blume et al.
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ACCEPTED MANUSCRIPT (1994) present a theoretical model to show that trading volume contains information in financial markets that cannot be obtained from stock prices alone, consistent with the
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widespread reliance on trading volume by technical analysts to predict price changes per se. Similarly, Llorente et al. (2002), predict that intensive trading volume will act as a signal to the
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market to forecast return autocorrelations.1Since within the CAPM framework, changes in betas should be closely related to returns, this motivates us to use trading volume as a
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potential explanatory variable for time variation in betas.
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Our focus on precious metal mining stocks is motivated by the fact this is a highly capital intensive industry and hence, cost of capital calculations can be particularly important. The
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industry also has other interesting aspects such as the fact that natural resource companies
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have to face a depleting resource base and also, they have compete while producing a rather homogeneous product. Since systematic risk should be associated with returns according to the
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CAPM, we also examine whether the linkage between trading volume and betas is reflected in
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volume-return relation.
In the empirical analysis, we utilize quantile regressions in addition to the conventional ordinary least squares (OLS). While ordinary least squares regressions are useful to specify the conditional mean response of a dependent variable to an independent variable, quantile regressions can help to determine whether there is a relation at the conditional median or
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As discussed in greater detail below, according to their model If high trading volume is caused by hedging (portfolio allocation), negative return autocorrelation is predicted. On the other hand, if speculation on private information, positive autocorrelation should be observed. Our analysis on the volume-return dynamics is also motivated by these approaches. 3
ACCEPTED MANUSCRIPT other quantiles. This can be particularly useful if there is a asymmetric relation between the variables exhibited at the extremes of the distribution.2
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As examples in recent work, both Chuang et al. (2009) and Gebka and Wohar (2013) demonstrate the potential usefulness of quantile regressions while investigating linkages
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between returns and trading volume. These authors show that there is Granger causality from
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trading volume to returns for a set of international equity markets not detected by conventional OLS regressions. Specifically, they find that there is positive causality from lagged
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volume to returns in higher quantiles but negative causality exists from volume to returns at
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lower quantiles.
Our sample consists of precious metals mining companies included in the Philadelphia
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Gold and Silver Index for the period between 2002 and 2014. We begin the analysis by
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estimating the time-varying betas by using the Kalman filter within the context of a state space framework. We discuss in detail why the Kalman filter is preferred to estimate time varying
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betas rather than other methods considered in the literature such as rolling OLS regressions or GARCH-based approaches. We then examine the relation between changes in betas and trading volume by both the OLS and quantile regressions.3 We find that there is a statistically significant relation between changes in betas and trading volume for approximately half of the firms in our sample. The relation is positive in the
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Quantile regression methods have been successfully applied in financial markets research in recent work. For example, Baur and Lucey (2010) examine whether gold acts as a hedge or safe haven for stocks and bonds by using quantile regression methods. Ciner et al. (2013) extend the same analysis to include oil and exchange rates along with gold similarly relying on quantile regression methods. 3 We de-trend trading volume for both linear and nonlinear effects as discussed further below. 4
ACCEPTED MANUSCRIPT majority of the cases, which is in general consistent with the notion that beta as a risk measure responds to trading volume. To determine whether there are undetected asymmetric linkages
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between the variables, we proceed to conduct the quantile regression analysis. This examination reveals that the relation indeed exhibits asymmetry in that higher (lower)
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quantiles trading volume has a positive (negative) relation with beta changes. 4
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As mentioned above, the CAPM predicts that beta changes should be closely associated with stock returns. Therefore, in the second part of the empirical analysis, we examine whether
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similar patterns are observed on linkages between trading volume and returns.5 We again rely on both OLS and quantile regressions, and the results point to several facts. First, again the
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application of the quantile regression method proves to be crucial in the analysis as the OLS
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results are never statistically significant between returns and trading volume. This is consistent
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with prior work in this branch of the literature.6 However, the quantile regressions reveal significant dependencies between the
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variables. Specifically, there is a negative relation between returns and volume at the lower ends of the quantile, i.e. for highly negative returns, while a positive relation exists at higher quantiles. Secondly, these findings for returns and trading volume are strongly consistent with
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As mentioned in the empirical analysis below, a caveat of the results is that the estimated coefficients are rather low, which is important to note for the economic significance of the findings. 5 This part of the analysis is also motivated by recent evidence on volume-return dynamics in stock markets, presented by both Chang et al. (2009) and Gebka and Wohar (2013). 6 This is consistent with many papers in the literature that find no relation between trading volume and returns, see Ciner (2002) as an example. 5
ACCEPTED MANUSCRIPT those reported recently by Chuang et al. (2009) and Gebka and Wohar (2013).7 Therefore, our results seem to point to a universal empirical regularity in financial markets. We argue that
Llorente et al. (2002), which is discussed in detail below.
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these findings are in fact consistent with the equilibrium volume-return model presented by
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We organize the rest of the paper as follows: In the next section, we present the data
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set. In Section 3, we discuss the statistical method of analysis and main findings of the paper. We present a discussion of the findings and offer concluding remarks in the final section of the
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paper.
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2. Data
The data set consists of stock prices of twenty six precious metals mining firms that are
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included in the Philadelphia Stock Exchange Gold and Silver Index. The analysis covers the
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period between July 30, 2002 and November 3, 2014. Some of the companies in the sample did
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not have data for the full sample period and their data spans are indicated in Table 1. The S&P 500 index is used as the market proxy in calculations of CAPM betas. Following Gallant et al. (1992), Hiemstra and Jones (1994), Ciner (2002) and more recently Gebka and Wohar (2013) we use the logarithm of daily number of shares traded, as our measure for trading volume. Sample summary statistics for returns, calculated as first differences of logarithms of closing prices, can be found in Table 2. It can be observed that returns are on average zero and tend to have negative skewness. Moreover, the returns show excess kurtosis for all of the 7
Chuang et al. (2000) also use quantile regression methods to test for causality from trading volume to return. However, their analysis slightly differs because rather than testing the relation at specific quantlles they examine causality for a range of quantiles. 6
ACCEPTED MANUSCRIPT companies, a phenomenon associated with nonlinearities in the return generating process and suggests heavy tails in return distributions. This is noteworthy because it indicates that the
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quantile regression methods could be suitable for the data of the study as this method is robust to outliers and also because it permits to examine whether the relation between trading
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volume and returns could be different in the tails of the distribution. Descriptive statistics for log trading volume are difficult to interpret and thus, not reported here. We have, however,
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tested for unit roots using the popular ADF and KPSS tests for both returns and trading volume
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and both variables can be characterized as stationary consistent with the literature. The results
3. Empirical Analysis
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3.1 Kalman Filter Betas
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of the unit root tests are available upon request.
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We begin the analysis by estimating OLS betas by using the familiar single factor market
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model egression, as stated below:
In which
(1)
denotes the return series of a precious metals mining stock in the samples and
specifies the market return, which is estimated by returns on the S&P 500 index. The OLS beta estimates are reported in Table 2. As argued above, the evidence in prior work suggests that betas are not constant and therefore, we test the stability of
coefficients in above
regression by utilizing the test developed by Bai and Perron (2003). These authors provide a Sup-F type test for the null hypothesis of no change in coefficients estimated by the OLS versus
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ACCEPTED MANUSCRIPT the alternative hypothesis of shifts in the coefficients. The Sup F-test statistics are also reported in Table 2 and consistent with prior work, constancy of betas is rejected for all but three of the
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companies in our sample.8
We proceed to model the time variation in betas to test for their linkage with trading
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volume. Time varying betas can be estimated by several methods such as a rolling window OLS
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regression, which has been used by several researchers in prior work, see for instance Fama and French (2006) for an application of this technique. In this paper, however, we follow the
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more recent work by Trecroci (2014) and Adrian Franzoni (2009) to estimate the time varying
(2)
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betas in a random coefficient framework that can be specified as follows:
(3)
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The above model can be conveniently estimated by the Kalman filter for each individual firm in
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the sample.9 This method is preferred in this paper over rolling regressions for several reasons. First, it is adaptive in nature. Secondly, in rolling OLS regressions the constant parameter assumption still has to be maintained within the chosen sample window, which is not required by the Kalman filter. Thirdly, empirical studies, such as Brooks et al. (1998) and Mergner and Bulla (2006), consistently report that the Kalman filter betas have superior out of sample forecasting power relative to betas estimated by rolling window OLS or GARCH methods. In Table 2, we also provide the mean, minimum and maximum of the Kalman filter betas for each
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For those companies, we only return-volume relations as mentioned in the next section of the paper. The residuals are assumed to be normally distributed. 8
ACCEPTED MANUSCRIPT of the stocks. It can be observed that the range between high and low betas is rather large, suggesting significant volatility. This indicates that an examination into the factors that impact
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fluctuation of betas could be of interest. 3.2 Betas and Trading Volume
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In the second step of the analysis, the Kalman filter betas are used to examine whether
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changes in CAPM betas are associated with trading volume in the precious metals mining sector. Before we conduct a regression analysis between the variables, we follow Gallant et al.
(4)
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by estimating the following equation:
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(1992) and Gebka and Wohar (2013) and adjust trading volume for linear and nonlinear trends
In the rest of the empirical analysis, the residuals ( ) from this regression are used as the
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trading volume variable. We do not report the results of this regression to converse space,
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however, similar to the studies mentioned above, we find that both linear and nonlinear trends are statistically significant and the R-squared of the regressions are approximately 20% on average. We proceed to test for a relation between changes in betas and trading volume for the gold mining stocks by estimating the following model, in which betas calculated as
stands for daily changes in
, by the OLS:
(5)
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ACCEPTED MANUSCRIPT The regression results are reported in Table 3 and we find that trading volume is indeed a determinant of variation in betas in more than half of the cases in our sample. And a significant
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majority of the statistically significant cases indicate a positive relation between change in betas and trading volume, consistent with the intuition of the study. However, it is important to note
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that the relation is estimated to be negative for three companies in our sample. Furthermore, the coefficients are rather small in each case, which makes it difficult to interpret the economic
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significance of the relation between beta variation and trading volume.
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We also examine whether there is a lagged relation between trading volume and Kalman filter betas. We run the same regression in (5) by including lagged volume as well as
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lagged returns to control for own effects. Information spillover from lagged trading volume to
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betas can exist if the adjustment to new information in the market is gradual rather than instantaneous, which would be consistent with the sequential information arrival model. The
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regression results are reported in Table 4 and we observe that for approximately half of the
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companies in our sample, there is evidence that lagged trading volume is positive and statistically significant.
The OLS analysis conducted above examines the average (mean) relations between the variables. Recent literature, however, shows that the linkages at the extremes, very high/low quantiles, can be different than the mean relations. In other words, trading volume may impact parts of the distribution of the betas other than the means. The quantile regression method is developed by Koenker and Bassett (1978) to capture this intuition by allowing an independent variable to impact a dependent variable at any quantile.
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ACCEPTED MANUSCRIPT The quantile regression analysis ultimately boils down to an optimization problem. Within the context of the regression model of interest in Equation (5), Koenker and Bassett
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(1978) show that the parameter b can be estimated for any quantile θ (0<θ<1) by minimizing
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the following argument:
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This expression indicates that the method involves the minimization of the sum of asymmetrically weighted absolute error terms (
with different weights for positive and
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negative residuals depending on the quantile chosen (Koenker and Hallock, 2001). The value of b for any θth regression quantile can be estimated by linear programming methods, the simplex
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method is used in the present paper, and standard errors can be bootstrapped.10 We conduct
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the minimization procedure at quantiles of θ=.05, .10, .50, .90 and .95 and thus, obtain quantile specific coefficient estimates. The quantile regression results tend to be useful at the extremes
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of the distributions, which motivates the choice of the specific quantiles used in the paper. In other words, we obtain the relation between beta changes and trading volume at the tails of the distribution of the former, not just the mean as the OLS provides. We first test for contemporaneous relations between daily beta changes and trading volume using the following quantile regression model:
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Many recent articles apply the quantile regression methodology to financial research, such as Baur and Lucey (2010) and Gebka and Wohar (2013).
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ACCEPTED MANUSCRIPT (6) is the θ-th quantile of the conditional distribution of
. The results are
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In which
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reported in Table 3. We now detect that all companies in our sample exhibits a statistically significant relation between changes in beta and trading volume in at least one of the quantiles
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reported. In the higher quantiles of .95 and .90, the relation is largely positive, while more
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negative coefficient estimates are obtained in lower quantiles of .05 and .10. This indicates that there is at least some asymmetry in the trading volume-beta change relation. In other words,
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large increases in systematic risk tend to be positively associated with trading volume, which
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has not been reported in the literature before to the best of our knowledge. This further lends support to the argument that trading volume conveys information to
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the market. However, the coefficients continue to be rather small. Moreover, we test whether
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the coefficients are equal across quantiles by means of a Wald test and report the test statistics along with their p-values also in Table 4. This analysis indicates that the null hypothesis of
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coefficient constancy is comfortably rejected in all but two cases, which further illustrates the importance for examining the full distribution of the dependent variable. We also examine whether there are lagged effects from trading volume to beta changes across the quantiles. To accomplish this, we included lagged trading volume, as well as lagged beta changes, in equation (6). The results of this analysis are reported in Table 5. We similarly report Wald tests on parameter constancy across the quantiles examined in this paper. For one third of the companies in the sample, the Wald tests are not statistically significant, which mean the null hypothesis of constant coefficients cannot be rejected. For the companies that 12
ACCEPTED MANUSCRIPT the Wald tests are significant, we find that lagged trading volume has negative covariance with beta changes in the negative tail of the distribution. On the other hand, highly positive beta
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changes are positively correlated with trading volume, similar to the results reported above. 3.3 Returns and Trading Volume
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It could be argued that the dynamic linkage between trading volume and changes in
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betas that is documented above should be observed between trading volume and returns as well if CAPM has empirical validity. Based on this intuition we proceed to examine the volume-
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return linkage of gold mining stocks. In the first part of the empirical analysis, we again examine
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the contemporaneous relation between volume and returns by the OLS and report the findings in Table 6.
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We find that returns do not have a statistically significant relation with trading volume,
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save for three companies in our sample. This is consistent with prior work, in which researchers
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generally find that returns do not co-vary with trading volume, see Karpoff (1987) for a survey, and Lee and Rui (2002) and Ciner (2002) for more recent empirical evidence. This is generally regarded as counter to the intuition of financial market practitioners who allude a special role to trading volume and also, to the implications of models by Blume et al. (1994) and Llorente et al. (2001), who show that trading volume can convey important information in markets as mentioned in the Introduction. Similar to the analysis conducted above, we proceed to examine the linkage between trading volume and return by utilizing the quantile regression approach. It is noteworthy that two recent papers also examine the relation between trading volume and returns and utilize 13
ACCEPTED MANUSCRIPT the quantile regression approach. Chuang et al. (2009) uses this technique to show that past trading volume has a positive (negative) effect on returns for the top (bottom) of the return
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distribution for the S&P 500 and FTSE 100 indices. Gebka and Wohar (2013) focus on the Pacific Basin equity markets and find that a very similar picture emerges. Since these studies focus on
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light on whether the findings can be generalized.
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market indexes and aggregate trading volume, our analysis of individual stock returns can shed
We first examine the contemporaneous relation between trading volume and returns by with returns in equation (6) and report the results in Table 6. The Wald test is
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replacing
statistically significant in each case, suggesting quantile dependency in regression coefficients.
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Furthermore, the results are uniform across the sample of companies. Returns in very lower
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quantiles (.05 and .10) have a negative relation with trading volume; on the other hand, returns in higher quantiles (.95 and .90) have a positive relation at comfortable statistical significance
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levels. Furthermore, the coefficients estimates are rather large in size, suggesting economic
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significance; however, this is only detected when the conditional quantiles are examined separately highlighting the importance of this method of analysis for this research question. These results are almost identical to those reported by Gebhka and Wohar (2013) and Chuang et al. (2009) by using international stock indices, suggesting the conclusion on volume-return dynamics could be universal. In Table 7, we report the quantile regression results for lagged trading volume. Again, the Wald test is statistically significant in each case. The results also indicate predictive power for trading volume for returns and moreover, the pattern of the findings is similar to those from
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ACCEPTED MANUSCRIPT lagged volume-beta linkage reported above, which suggests an association between returns and CAPM betas as predicted by the theory. Returns in lower quantiles always have a negative
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relation with lagged volume, while returns in higher quantiles exhibit a positive linkage for each case company in our sample.
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4. Discussion and Concluding Remarks
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As mentioned above, in recent work, Chuang et al. (2009) and Geb kha and Wohar (2013) also investigate volume-return relations in financial markets by relying on stock index
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data. Our results are almost identical to their findings; hence, volume-return relations revealed
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by quantile regression seem to be a universal phenomenon in financial markets. Therefore, a discussion of the theoretical underpinnings of the empirically observed volume-return quantile
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regression results may be relevant. In particular, while Chuang et al. (2009) suggest that no
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equlibirium model can presently explain the volume-return quantile regression causality empirics, Gebkha and Wohar (2013) forcefully argue that the model by Llorente et al. (2002) is
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consistent with the findings.
Llorenta et al. (2002) build on the work by Wang (1994) and Campbell et al. (1993) to study the role of trading volume in explaining stock return autocorrelations. The underlying intuition of their model is that intensive trading volume occurs either as a result of hedging (portfolio allocation) or speculation (based on private information) by market participants. If hedging is the primary motive to trade, negative return autocorrelations will be observed. That is because investors will sell (buy) at a lower price relative to the fundamental value to accommodate their hedging needs and the price will revert back to the fundamental value in 15
ACCEPTED MANUSCRIPT the next session. However, if speculation is the primary reason to trade, then positive return autocorrelations will be observed. That is because if the underlying private information that
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generated the speculative trade will require more than one period to be fully incorporated into the price.
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Gebka and Wohar (2013) argue that the quartile regression causality results are
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consistent with the above implications. If speculation on positive private information is the primary motive to trade, returns will likely be from higher quantiles today with increased
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trading volume and one should observe a positive relation between volume and returns. A similar implication holds if selling pressure for hedging is the main reason to trade. Hedging
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pressure will generate intensive trading and lower prices today to make the stock attractive for
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buyers. However, the stock price will revert back to its fundamental value in the next period generating returns likely from higher quantiles. Thus, a positive relation will be observed
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between trading volume and returns from higher quantiles. If, on the other hand, intensive
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trading is due to hedging pressure to buy, next period return will likely be from lower quantiles, since there will be decline in price back to fundamental value. In this case, it is implied that a negative relation between trading volume and returns from lower quantiles will be observed. As the final case, if a low quantile return occurs because of negative private information, similarly negative causality from volume to return will observed since it will take more than one period for the negative information to be incorporated into pricing. Our empirical findings, as well as those of Chuang et al. (2009), are entirely consistent with the implications of tis equilibrium model. Furthermore, our study also shows that the
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ACCEPTED MANUSCRIPT relation between trading volume and returns is at least somewhat replicated in the linkage between beta and trading volume. This finding lends more support to the role of trading
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volume in financial markets and also suggests that betas and returns are at least somewhat associated, as implied by CAPM for the sample of precious metals firms studied in this article. It
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beta are also valid in other markets and industries.
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would of interest to examine in future research whether the conclusions on trading volume and
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ACCEPTED MANUSCRIPT Table 1- Precious Metals Mining Firms
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Data Span 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 11/28/2006- 11/3/2014 5/10/2007- 11/3/2014 7/30/2002- 11/3/2014 9/4/2003- 11/3/2014 1/12/2004- 11/3/2014 7/18/2005- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 1/23/2003= 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 9/14/2006- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/15/2003- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 11/18/2004- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 4/20/2003- 11/3/2014 7/6/2005- 11/3/2014 7/30/2002- 11/3/2014 5/12/2005- 11/3/2014
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Name Barrick Gold Corp. Angle Eagle Mines Ltd. First Majestic Silver Corp. Allied Nevada Gold Corp. AngleGold Ashanti Ltd. AuRico Gold Inc. Yamana Gold Inc. Banro Corp. Buenaventura Gold Corp. Coeur Mining, Inc. Eldorado Gold Corp. Freeport McMoran, Inc. Gold Fields Ltd. Goldcorp, Inc. Rangold Resources Ltd. Gold Resource Corp. Hecla Mining Co. Harmony Gold Mining Co. Iamgold Corp. Kinross Gold Corp. McEwen Mining, Inc. Newmont Mining Corp. New Gold, Inc. Pan American Silver Corp. Royal Gold, Inc. Seabridge God, Inc. Silver Wheaton Corp. Silver Standard Resources, Inc. Tanzanian Royalty Exploration, Inc.
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Symbol ABX AEM AG ANV AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Note- The data set includes the precious metal mining companies that are included in the Philadelphia Gold and Silver Index.
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ACCEPTED MANUSCRIPT Table 2- Summary Statistics: Returns
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Mean Std. Dev. Skewness Kurtosis ABX -.000 .026 .202 7.604 AEM .000 .031 -.551 7.619 AG .000 .043 -.051 2.985 ANV .001 .050 .511 12.502 AU -.000 .029 .515 10.063 AUQ -.000 .039 -.127 3.845 AUY .000 .034 -.167 3.713 BAA -.000 .100 14.372 466.06 BVN .000 .030 -.384 4.767 CDE -.000 .041 -.025 7.176 EGO .000 .036 -.070 6.614 FCX .000 .031 -.477 5.644 GFI -.000 .031 .236 9.116 GG .000 .029 .101 4.883 GOLD .001 .030 .208 4.226 GORO .000 .040 -.034 8.547 HL -.000 .041 -.284 6.504 HMY -.000 .033 .219 5.346 IAG -.000 .033 -.129 5.709 KGC -.000 .032 .033 4.645 MUX .000 .060 1.072 12.535 NEM -.000 .024 .270 6.911 NGD -.000 .043 .949 38.134 PAAS .000 .032 .097 4.851 RGLD .000 .028 -.696 13.549 SA .000 .039 .190 4.589 SLW .000 .036 -.274 4.780 SSRI .000 .037 .039 3.868 TRX .000 .043 .055 7.429 Note- This table provides the descriptive statistics for the returns of the precious metals mining firms included in the data set. Returns are calculated as first differences of logarithms of daily closing stock prices.
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ACCEPTED MANUSCRIPT
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-.09 -.07 .88 .64 .77 .89 .81 .89 1.20 .98 .81
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-.96 -.53 -.70 -1.31 -.51 -.30 -.57 -.46 -.47 -.54 -.53 -.28 -.81 -.74 -.57 -1.43 -.49 -2.68 -.42 -.52 -.26 -.86 -.80 -.02
.63 .02 2.33 .15 .11 .16 .81 -.05 .36 .33 .50 -.04 3.12
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-.10 -.14 .85 -.27 -.15 -.10 -.025 -.16 -.07 -.10 -.02 -.14 1.39
Max. .55 .73
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Min. -1.01 -1.36
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ABX AEM AG ANV AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Mean -.04 -.47
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Table 3- Summary Statistics: Betas
.31 .58 2.18 1.71 11.36 1.88 2.41 2.21 2.63 2.16 1.67
OLS -.12 -.18 -.19 -.095 -.11 -.15 .79 -.05 -.21 -.17 -.18 -.21 -.094 -.15 -.09 -.16 1.22 -.11 -.22 -.16 .19 .57 .93 .77 .51 .65 1.04 .82 .63
Bai-Perron 18.75 (.00) 18.91 (.00) 6.43 (.50) 9.83 (.15) 15.34 (.01) 25.15 (.00) 31.61 (.00) 53.24 (.00) 16.27 (.00) 17.79 (.00) 50.20 (.00) 11.46 (.08) 24.73 (.00) 19.87 (.00) 36.92 (.00) 53.00 (.00) 90.81 (.00) 8.62 (.24) 38.03 (.00) 31.22 (.00) 625.49 (.00) 73.09 (.00) 18.53 (.00) 66.99 (.00) 47.79 (.00) 36.20 (.00) 47.67 (.00) 105.95 (.00) 32.87 (.00)
Note- This table provides the descriptive statistics for the Kalman filter betas estimated by equations (2)(3) as well as thehe Bai-Perron test for coefficient constancy in equation (1)..
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ACCEPTED MANUSCRIPT Table 4- Trading Volume and Beta: Contemporaneous Relations
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Median -.000 (.16) .008 (.02) .000 (.06) -.000 (.00) -.000 (.28) -.000 (.02) .000 (.00) .000 (.00) -.000 (.00) .000 (.00) .000 (.00) .000 (.00) .000 (.04) -.000 (.00) .000 (.16) .000 (.00) .000 (.00) -.000 (.21) .000 (.19) -.002 (.26) .001 (.00) .002 (.00) -.000 (.31) -.000 (.94) .002 (.00) .000 (.00)
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OLS -.000 (.74) -.000 (.98) .000 (.24) -.000 (.00) -.000 (.93) -.000 (.41) .000 (.00) .000 (.00) -.000 (.04) .000 (.00) .000 (.00) .000 (.00) .000 (.00) -.000 (.09) -.000 (.12) .000 (.00) .000 (.00) -.000 (.33) .000 (.17) -.002 (.69) .001 (.00) .002 (.00) -.001 (.35) -.001 (.02) .002 (.00) .000 (.00)
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.10 -.006 (.00) -.006 (.01) -.004 (.00) -.000 (.00) -.004 (.00) .000 (.00) .001 (.02) .000 (.00) -.000 (.00) .000 (.00) .000 (.00) -.000 (.00) .000 (.75) -.000 (.05) -.006 (.00) -.000 (.00) .000 (.00) .000 (.01) -.001 (.31) -.049 (.00) .002 (.00) .000 (.75) -.001 (.00) -.005 (.00) -.001 (.04) .000 (.03)
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.05 -.010 (.00) -.008 (.01) -.007 (.00) -.000 (.00) -.007 (.00) .000 (.60) .000 (.00) .000 (.00) -.001 (.00) .000 (.00) -.000 (.00) -.000 (.00) .000 (.42) .000 (.85) -.009 (.00) -.000 (.00) .000 (.00) .000 (.04) -.002 (.26) -.084 (.00) .003 (.00) .002 (.00) -.001 (.00) -.003 (.31) -.002 (.06) .000 (.02)
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ABX AEM AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Wald test 500.98 (.00) 312.87 (.00) 283.19 (.00) 163.74 (.00) 147.32 (.00) 78.77 (.00) 63.41 (.00) 297.82 (.00) 19.25 (.00) 70.89 (.00) 396.50 (.00) 295.32 (.00) 13.43 (.00) 34.53 (.00) 112.33 (.00) 240.94 (.00) 284.92 (.00) 32.31 (.00) 42.10 (.00) 109.74 (.00) 7.41 (.11) 105.04 (.00) 13.34 (.00) 29.19 (.00) 66.91 (.00) 8.86 (.07)
.90 .007 (.00) .006 (.01) .006 (.00) .000 (.00) .003 (.00) -.000 (.00) .000 (.00) -.000 (.00 -.000 (.01) .000 (.00) .000 (.00) .001 (.00) .000 (.00) .000 (.43) .002 (.00) .000 (.24) .001 (.00) -.000 (02) .003 (.00) .041 (.00) .001 (.00) .004 (.00) .001 (.08) -.000 (.78) .005 (.00) .000 (.42)
.95 .010 (.00) .011 (.00) .008 (.00) .000 (.00) .008 (.00) -.000 (.03) .000 (.00) -.000 (.00) -.000 (.98) .000 (.00) .001 (.00) .001 (.00) .000 (.00) -.000 (.27) .000 (.67) .000 (.01) .002 (.00) -.000 (.00) .008 (.00) .059 (.00) .002 (.08) .005 (.08) .000 (.72) .003 (.12) .006 (.08) -.000 (.57)
Note- OLS estimates are from equation (5) and examine the contemporaneous relation between trading volume and the Kalman filter betas. The quantile regression estimates are from equation (6) and test for the contemporaneous relation between the variables at specific quantiles. The p-values are in parentheses. The null hypothesis of the Wald test is equal coefficients across the quantiles.
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ACCEPTED MANUSCRIPT Table 5- Trading Volume and Beta: Lagged Relations
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Median -.000 (.76) -.000 (.40) .000 (.49) .000 (.21) .000 (.63) .000 (.00) .000 (.28) .000 (.70) .000 (.71) .000 (.14) .000 (.38) .000 (.03) .000 (.72) .000 (.82) .000 (.70) .000 (.12) -.000 (.17) .000 (.07) .000 (.35) .000 (.87) .000 (.95) -.000 (.09) -.000 (.73) .000 (.94) -.000 (.67) -.000 (.23)
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OLS -.000 (.44) .000 (.86) .000 (.33) -.000 (.00) -.000 (.69) -.000 (.52) .000 (.00) .000 (.00) -.000 (.05) .000 (.00) .000 (.00) .000 (.00) .000 (.00) -.000 (.06) -.000 (.19) .000 (.00) -.000 (.52) .000 (.00) .001 (.08) .001 (.86) .001 (.00) .002 (.00) .000 (.58) -.001 (.11) .002 (.00) .000 (.00)
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.10 -.002 (.00) -.002 (.00) -.002 (.00) -.000 (.00) -.001 (.00) -.000 (.57) -.000 (.38) .000 (.35) -.000 (.51) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.05) -.001 (.00) -.000 (.00) -.000 (.04) -.000 (.00) -.002 (.00) -.034 (.00) -.000 (.42) -.000 (.00) -.000 (.00) -.000 (.05) -.000 (.00) -.000 (.45)
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.05 -.004 (.00) -.004 (.00) -.003 (.00) -.000 (.00) -.003 (.00) -.000 (.11) -.000 (.15) .000 (.18) .000 (.98) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.18) -.003 (.00) -.000 (.00) -.000 (.02) -.000 (.00) -.004 (.00) -.061 (.00) .000 (.97) -.001 (.00) -.000 (.00) -.002 (.00) -.002 (.00) .000 (.33)
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ABX AEM AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL IAG MUX KGC NEM NGD PAAS RGLD SA SLW SSRI TRX
Wald test 220.67 (.00) 241.99 (.00) 144.42 (.00) 28.32 (.06) 144.61 (.00) 19.03 (.24) 6.00 (.19) 8.23 (.08) 1.79 (.77) 137.28 (.00) 93.15 (.00) 214.98 (.00) 3.20 (.52) 10.61 (.91) 62.88 (.00) 36.54 (.00) 4.99 (.28) 53.41 (.00) 73.91 (.00) 90.85 (.00) 5.24 (.26) 106.34 (.00) 34.74 (.00) 107.27 (.00) 14.12 (.13) 7.87 (.10)
.90 .002 (.00) .002 (.00) .002 (.00) .000 (.00) .001 (.00) .000 (.05) .000 (.04) -.000 (.16) .000 (.41) .000 (.00) .000 (.00) .000 (.00) .000 (.00) .000 (.20) .001 (.00) .000 (.00) -.000 (.37) .000 (.00) .003 (.00) .036 (.00) .000 (.11) .001 (.00) .000 (.00) .001 (.00) .000 (.19) -.000 (.98)
.95 .004 (.00) .004 (.00) .003 (.00) .000 (.00) .003 (.00) .000 (.00) .000 (.02) -.000 (.03) .000 (.33) .000 (.00) .000 (.00) .000 (.00) .000 (.00) .000 (.25) .003 (.00) .000 (.00) -.000 (.38) .000 (.00) .006 (.00) .061 (.00) .000 (.44) .002 (.00) .000 (.00) .003 (.00) .000 (.05) .000 (.43)
Note- OLS estimates are from equation (5) and quantile regression estimates are obtained from equation (6), both obtained by included lagged trading volume in the models. The null hypothesis of the Wald test is equal coefficients across the quantiles.
Table 6- Trading Volume and Returns: Contemporaneous Relations
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Wald test 800.11 (.00) 864.33 (.00) 164.39 (.00) 69.31 (.00) 823.30 (.00)
.05 -.025 (.00) -.026 (.00) -.015 (.00) -.015 (.04) -.029 (.00)
.10 -.020 (.00) -.023 (.00) -.013 (.00) -.015 (.01) -.023 (.00)
OLS -.000 (.29) -.001 (.15) -.001 (.27) .004 (.09) .000 (.48)
Median .000 (.44) .001 (.31) -.000 (.70) .000 (.21) .000 (.83)
.90 .020 (.00) .024 (.00) .010 (.00) .020 (.00) .023 (.00)
.95 .023 (.00) .030 (.00) .010 (.00) .023 (.00) .029 (.00) 24
ACCEPTED MANUSCRIPT
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.000 (.68) .000 (.99) -.000 (.00) .001 (.04) .001 (.27) .000 (.99) .001 (.11) .000 (.57) .000 (.63) .000 (.37) .000 (.99) .000 (.99) .001 (.37) .001 (.11) -.000 (.99) .000 (.99) -.000 (.61) .000 (.20) -.000 (.84) -.000 (.69) .003 (.82) .000 (.80) -.000 (.96) -.000 (.99)
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-.000 (.85) -.001 (.29) .004 (.06) -.000 (.91) .001 (.35) .001 (.29) -.003 (.00) .000 (.70) -.001 (.23) .001 (.05) .000 (.92) .000 (.94) -.000 (.82) -.000 (.66) .005 (.00) -.000 (.65) -.001 (.12) -.000 (.97) -.000 (.80) -.001 (.18) .003 (.00) -.001 (.35) -.001 (.40) -.000 (.74)
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-.020 (.00) -.017 (.00) -.017 (.00) -.019 (.00) -.022 (.00) -.017 (.00) -.025 (.00) -.018 (.00) -.022 (.00) -.010 (.00) -.017 (.00) -.022 (00) -.024 (.00) -.015 (.00) -.007 (.00) -.022 (.00) -.025 (.00) -.008 (.00) -.021 (.00) -.019(.00) -.014 (.00) -.023 (.00) -.024 (.00) -.019 (.00)
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-.030 (.00) -.024 (.00) -.025 (.00) -.023 (.00) -.024 (.00) -.020 (.00) -.034 (.00) -.022 (.00) -.027 (.00) -.011 (.00) -.020 (.00) -.030 (.00) -.028 (.00) -.019 (.00) -.008 (.00) -.026 (.00) -.030 (.00) -.009 (.00) -.027 (.00) -.022 (.00) -.019 (.00) -.028 (.00) -.032 (.00) -.025 (.00)
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362.31 (.00) 538.03 (.00) 974.87 (.00) 1148.46 (.00) 300.07 (.00) 241.45 (.00) 502.23 (.00) 481.19 (.00) 863.13 (.00) 217.97 (.00) 434.72 (.00) 381.87 (.00) 513.92 (.00) 459.75 (.00) 174.34 (.00) 388.17 (.00) 1614.20 (.00) 366.79 (.00) 525.51 (.00) 633.68 (.00) 586.38 (.00) 525.60 (.00) 823.03 (.00) 246.92 (.00)
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AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG MUX KGC NEM NGD PAAS RGLD SA SLW SSRI TRX
.022 (.00) .018 (.00) .025 (.00) .021 (.00) .022 (.00) .020 (.00) .020 (.00) .020 (.00) .021 (.00) .011 (.00) .019 (.00) .024 (.00) .024 (.00) .014 (.00) .014 (.00) .022 (.00) .023 (.00) .010 (.00) .021 (.00) .020 (.00) .020 (.00) .022 (.00) .025 (.00) .019 (.00)
.024 (.00) .022 (.00) .032 (.00) .026 (.00) .027 (.00) .022 (.00) .025 (.00) .024 (.00) .027 (.00) .012 (.00) .024 (.00) .032 (.00) .030 (.00) .018 (.00) .016 (.00) .027 (.00) .028 (.00) .013 (.00) .028 (.00) .026 (.00) .024 (.00) .027 (.00) .030 (.00) .025 (.00)
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Note- OLS and quantile regression estimates are provided for the relation between returns and trading volume. The p-values are in parentheses. The null hypothesis of the Wald test is equal coefficients across quantiles
Table 7- Trading Volume and Returns: Lagged Relations
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Wald test 402.91 (.00) 154.65 (.00) 47.62 (.00) 51.13 (.00) 32.74 (.00) 42.16 (.00)
.05 -.016 (.00) -.031 (.00) -.004 (.01) -.010 (.06) -.012 (.00) -.007 (.03)
.10 -.010 (.00) -.009 (.00) -.003 (.16) .000 (.94) -.008 (.00) -.005 (.00)
OLS -.000 (.53) .000 (.81) -.000 (.59) .000 (.99) .001 (.27) .000 (.99)
Median -.000 (.90) .001 (.15) -.001 (.38) -.000 (.69) .000 (.84) .000 (.59)
.90 .009 (.00) .011 (.00) .003 (.07) -.000 (.80) .008 (.00) .008 (.00)
.95 .012 (.00) .016 (.00) .004 (.09) .000 (.95) .011 (.00) .009 (.00) 25
ACCEPTED MANUSCRIPT
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-.000 (.99) -.000 (.99) .001 (.26) .000 (.51) -.000 (.81) .000 (.91) -.001 (.20) -.000 (.88) -.000 (.69) .000 (.99) -.001 (.28) .001 (.35) .000 (.39) -.003 (.02) -.001 (.52) .001 (.34) .000 (.15) -.001 (.26) -.002 (.06) .001 (.21) .001 (.86) -.001 (.30) -.000 (.79)
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-.001 (.10) .004 (.06) .000 (.39) .000 (.76) -.001 (.23) .000 (.51) -.001 (.13) -.000 (.43) -.000 (.89) .002 (.08) -.000 (.89) -.000 (.86) -.000 (.59) -.002 (.03) -.001 (.10) -.000 (.99) .001 (.15) -.003 (.02) -.002 (.08) .002 (.01) -.000 (.86) -.003 (.02) -.000 (.97)
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-..009 (.00) -.009 (.02) -.009 (.00) -.007 (.02) -.003 (.05) -.014 (.00) -.012 (.00) -.010 (.00) -.005 (.00) -.002 (.34) -.010 (.00) -.009 (.00) -.008 (.00) -.001 (.00) -.003 (.05) -.006 (.00) -.005 (.00) -.007 (.00) -.009 (.00) -.003 (.04) -.012 (.00) -.012 (.00) -.010 (.00)
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-.012 (.00) -.019 (.00) -.009 (.00) -.009 (.00) -.004 (.10) -.012 (.00) -.013 (.00) -.015 (.00) -.007 (.00) .001 (.65) -.021 (.03) -.013 (.00) -.001 (.00) -.014 (.00) -.005 (.00) -.013 (.00) -.008 (.00) -.008 (.00) -.010 (.00) -.006 (.00) -.021 (.00) -.014 (.00) -.011 (.00)
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117.56 (.00) 69.13 (.00) 57.70 (.00) 337.47 (.00) 19.17 (,00) 67.23 (.00) 300.55 (.00) 311.75 (.00) 12.67 (.01) 48.84 (.01) 121.31 (.00) 128.13 (.00) 214.12 (.00) 347.44 (.00) 32.45 (.00) 25.02 (.00) 92.32 (.00) 4.07 (.04) 82.06 (.00) 10.88 (.02) 30.44 (.03) 85.07 (.00) 10.38 (.03)
.006 (.00 .015 (.00) .009 (.00) .003 (.14) -.000 (.75) .012 (.00) .007 (.01) .007 (.00) .006 (.00) .004 (.08) .006 (.00) .009 (.00) .004 (.02) .004 (.01) .000 (.76) .004 (.04) .006 (.00) .001 (.57) .007 (.00) .009 (.00) .006 (.01) .001 (.48) .008 (.00)
.007 (.00) .025 (.00) .016 (.00) .003 (.28) -.002 (.35) .017 (.00) .009 (.00) .011 (.00) .008 (.00) .008 (.03) .010 (.00) .013 (.00) .007 (.01) .008 (.00) -.003 (.40) .008 (.00) .010 (.00) -.001 (.64) .008 (.00) .011 (.00) .010 (.00) .005 (.09) .013 (.00)
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AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Note- OLS and quantile regression estimates are provided in this table for the predictive power of
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lagged trading volume for returns. The p-values are in parentheses. The null hypothesis of the Wald test is equal coefficients across quantiles.
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ACCEPTED MANUSCRIPT Highlights
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Explanatory power of trading volume is examined for both time varying CAPM betas and stock returns for the precious metals mining sector Quantile regressions indicate asymmetric dynamics between the variables Returns from higher (lower) quantiles have a positive (negative) linkage with both contemporaneous and lagged trading volume Results on volume-return relation is consistent with equilibrium models on return autocorrelations
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S1057-5219(15)00030-7 doi: 10.1016/j.irfa.2015.01.019 FINANA 809
To appear in:
International Review of Financial Analysis
Please cite this article as: Ciner, C., Time Variation in Systematic Risk, Returns and Trading Volume: Evidence from Precious Metals Mining Stocks, International Review of Financial Analysis (2015), doi: 10.1016/j.irfa.2015.01.019
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Time Variation in Systematic Risk, Returns and Trading Volume:
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Evidence from Precious Metals Mining Stocks
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Cetin Ciner Professor Finance Department of Economics and Finance Cameron School of Business University of North Carolina Wilmington E-mail: [email protected]
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January 17, 2015
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Abstract: We investigate whether trading volume has explanatory power for time variation in CAPM betas as well as returns, for the precious metals mining sector. We show that significant dependencies exist between these variables; however, empirical linkages are only revealed when quantile regression method is employed. The observed dynamics are particularly strong between trading volume and returns. We find that returns from lower (higher) quantiles have a negative (positive) relation with volume. We discuss the consistency of this asymmetric relation with equilibrium volume-return autocorrelation models suggested in prior work. JEL Classification: G0, G15 Keywords: trading volume, quantile regression, returns, beta
I am grateful to comments by two referees, which significantly improved this study. All remaining errors are my responsibility. Time Variation in Systematic Risk, Returns and Trading Volume: Evidence from Gold Mining Stocks 1. Introduction
ACCEPTED MANUSCRIPT Beta, as the sole measure of systematic risk according to the Capital Asset Pricing Model (CAPM), occupies a central role in modern finance theory. Financial researchers as well as
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market practitioners rely on the beta coefficient to correctly value stocks, to calculate the cost of capital of a corporation and also, to evaluate the performance of portfolio managers. In the
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context of the CAPM, beta is assumed to be constant over time and therefore, can be easily estimated. However, financial researchers, beginning by the early work by Sharpe et al. (1974),
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and Fabozzi and Francis (1978), have consistently argued that observed betas are not constant,
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rather they exhibit significant variation through time.
Subsequent research in this area has largely focused on the impact of macroeconomic
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variables, such as industrial production and inflation, to explain the time variation in betas.
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Recent examples of this strand of the literature include Mergner and Bulla (2008), Andersen et al. (2005) and Lettau and Ludvingson (2001) among others. Unfortunately, a common
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conclusion of these articles is that macroeconomic variables have little explanatory power for
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understanding the time variation in individual stock betas. In this paper, we further investigate the time variation in betas by adopting a view towards microeconomic, rather than macroeconomic, factors. As a novel addition to the literature, we examine whether trading volume can explain the observed time variation in systematic risk of stocks in the precious metals mining sector. Our hypothesis that trading volume can explain time-variation in CAPM betas stems from market microstructure models, such as the well-known mixture of distributions hypothesis, which assign a special importance to trading volume, as a proxy for the rate of information flow to the market. Also, Blume et al.
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ACCEPTED MANUSCRIPT (1994) present a theoretical model to show that trading volume contains information in financial markets that cannot be obtained from stock prices alone, consistent with the
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widespread reliance on trading volume by technical analysts to predict price changes per se. Similarly, Llorente et al. (2002), predict that intensive trading volume will act as a signal to the
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market to forecast return autocorrelations.1Since within the CAPM framework, changes in betas should be closely related to returns, this motivates us to use trading volume as a
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potential explanatory variable for time variation in betas.
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Our focus on precious metal mining stocks is motivated by the fact this is a highly capital intensive industry and hence, cost of capital calculations can be particularly important. The
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industry also has other interesting aspects such as the fact that natural resource companies
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have to face a depleting resource base and also, they have compete while producing a rather homogeneous product. Since systematic risk should be associated with returns according to the
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CAPM, we also examine whether the linkage between trading volume and betas is reflected in
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volume-return relation.
In the empirical analysis, we utilize quantile regressions in addition to the conventional ordinary least squares (OLS). While ordinary least squares regressions are useful to specify the conditional mean response of a dependent variable to an independent variable, quantile regressions can help to determine whether there is a relation at the conditional median or
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As discussed in greater detail below, according to their model If high trading volume is caused by hedging (portfolio allocation), negative return autocorrelation is predicted. On the other hand, if speculation on private information, positive autocorrelation should be observed. Our analysis on the volume-return dynamics is also motivated by these approaches. 3
ACCEPTED MANUSCRIPT other quantiles. This can be particularly useful if there is a asymmetric relation between the variables exhibited at the extremes of the distribution.2
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As examples in recent work, both Chuang et al. (2009) and Gebka and Wohar (2013) demonstrate the potential usefulness of quantile regressions while investigating linkages
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between returns and trading volume. These authors show that there is Granger causality from
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trading volume to returns for a set of international equity markets not detected by conventional OLS regressions. Specifically, they find that there is positive causality from lagged
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volume to returns in higher quantiles but negative causality exists from volume to returns at
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lower quantiles.
Our sample consists of precious metals mining companies included in the Philadelphia
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Gold and Silver Index for the period between 2002 and 2014. We begin the analysis by
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estimating the time-varying betas by using the Kalman filter within the context of a state space framework. We discuss in detail why the Kalman filter is preferred to estimate time varying
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betas rather than other methods considered in the literature such as rolling OLS regressions or GARCH-based approaches. We then examine the relation between changes in betas and trading volume by both the OLS and quantile regressions.3 We find that there is a statistically significant relation between changes in betas and trading volume for approximately half of the firms in our sample. The relation is positive in the
2
Quantile regression methods have been successfully applied in financial markets research in recent work. For example, Baur and Lucey (2010) examine whether gold acts as a hedge or safe haven for stocks and bonds by using quantile regression methods. Ciner et al. (2013) extend the same analysis to include oil and exchange rates along with gold similarly relying on quantile regression methods. 3 We de-trend trading volume for both linear and nonlinear effects as discussed further below. 4
ACCEPTED MANUSCRIPT majority of the cases, which is in general consistent with the notion that beta as a risk measure responds to trading volume. To determine whether there are undetected asymmetric linkages
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between the variables, we proceed to conduct the quantile regression analysis. This examination reveals that the relation indeed exhibits asymmetry in that higher (lower)
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quantiles trading volume has a positive (negative) relation with beta changes. 4
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As mentioned above, the CAPM predicts that beta changes should be closely associated with stock returns. Therefore, in the second part of the empirical analysis, we examine whether
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similar patterns are observed on linkages between trading volume and returns.5 We again rely on both OLS and quantile regressions, and the results point to several facts. First, again the
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application of the quantile regression method proves to be crucial in the analysis as the OLS
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results are never statistically significant between returns and trading volume. This is consistent
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with prior work in this branch of the literature.6 However, the quantile regressions reveal significant dependencies between the
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variables. Specifically, there is a negative relation between returns and volume at the lower ends of the quantile, i.e. for highly negative returns, while a positive relation exists at higher quantiles. Secondly, these findings for returns and trading volume are strongly consistent with
4
As mentioned in the empirical analysis below, a caveat of the results is that the estimated coefficients are rather low, which is important to note for the economic significance of the findings. 5 This part of the analysis is also motivated by recent evidence on volume-return dynamics in stock markets, presented by both Chang et al. (2009) and Gebka and Wohar (2013). 6 This is consistent with many papers in the literature that find no relation between trading volume and returns, see Ciner (2002) as an example. 5
ACCEPTED MANUSCRIPT those reported recently by Chuang et al. (2009) and Gebka and Wohar (2013).7 Therefore, our results seem to point to a universal empirical regularity in financial markets. We argue that
Llorente et al. (2002), which is discussed in detail below.
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these findings are in fact consistent with the equilibrium volume-return model presented by
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We organize the rest of the paper as follows: In the next section, we present the data
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set. In Section 3, we discuss the statistical method of analysis and main findings of the paper. We present a discussion of the findings and offer concluding remarks in the final section of the
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paper.
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2. Data
The data set consists of stock prices of twenty six precious metals mining firms that are
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included in the Philadelphia Stock Exchange Gold and Silver Index. The analysis covers the
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period between July 30, 2002 and November 3, 2014. Some of the companies in the sample did
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not have data for the full sample period and their data spans are indicated in Table 1. The S&P 500 index is used as the market proxy in calculations of CAPM betas. Following Gallant et al. (1992), Hiemstra and Jones (1994), Ciner (2002) and more recently Gebka and Wohar (2013) we use the logarithm of daily number of shares traded, as our measure for trading volume. Sample summary statistics for returns, calculated as first differences of logarithms of closing prices, can be found in Table 2. It can be observed that returns are on average zero and tend to have negative skewness. Moreover, the returns show excess kurtosis for all of the 7
Chuang et al. (2000) also use quantile regression methods to test for causality from trading volume to return. However, their analysis slightly differs because rather than testing the relation at specific quantlles they examine causality for a range of quantiles. 6
ACCEPTED MANUSCRIPT companies, a phenomenon associated with nonlinearities in the return generating process and suggests heavy tails in return distributions. This is noteworthy because it indicates that the
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quantile regression methods could be suitable for the data of the study as this method is robust to outliers and also because it permits to examine whether the relation between trading
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volume and returns could be different in the tails of the distribution. Descriptive statistics for log trading volume are difficult to interpret and thus, not reported here. We have, however,
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tested for unit roots using the popular ADF and KPSS tests for both returns and trading volume
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and both variables can be characterized as stationary consistent with the literature. The results
3. Empirical Analysis
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3.1 Kalman Filter Betas
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of the unit root tests are available upon request.
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We begin the analysis by estimating OLS betas by using the familiar single factor market
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model egression, as stated below:
In which
(1)
denotes the return series of a precious metals mining stock in the samples and
specifies the market return, which is estimated by returns on the S&P 500 index. The OLS beta estimates are reported in Table 2. As argued above, the evidence in prior work suggests that betas are not constant and therefore, we test the stability of
coefficients in above
regression by utilizing the test developed by Bai and Perron (2003). These authors provide a Sup-F type test for the null hypothesis of no change in coefficients estimated by the OLS versus
7
ACCEPTED MANUSCRIPT the alternative hypothesis of shifts in the coefficients. The Sup F-test statistics are also reported in Table 2 and consistent with prior work, constancy of betas is rejected for all but three of the
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companies in our sample.8
We proceed to model the time variation in betas to test for their linkage with trading
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volume. Time varying betas can be estimated by several methods such as a rolling window OLS
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regression, which has been used by several researchers in prior work, see for instance Fama and French (2006) for an application of this technique. In this paper, however, we follow the
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more recent work by Trecroci (2014) and Adrian Franzoni (2009) to estimate the time varying
(2)
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betas in a random coefficient framework that can be specified as follows:
(3)
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The above model can be conveniently estimated by the Kalman filter for each individual firm in
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the sample.9 This method is preferred in this paper over rolling regressions for several reasons. First, it is adaptive in nature. Secondly, in rolling OLS regressions the constant parameter assumption still has to be maintained within the chosen sample window, which is not required by the Kalman filter. Thirdly, empirical studies, such as Brooks et al. (1998) and Mergner and Bulla (2006), consistently report that the Kalman filter betas have superior out of sample forecasting power relative to betas estimated by rolling window OLS or GARCH methods. In Table 2, we also provide the mean, minimum and maximum of the Kalman filter betas for each
8 9
For those companies, we only return-volume relations as mentioned in the next section of the paper. The residuals are assumed to be normally distributed. 8
ACCEPTED MANUSCRIPT of the stocks. It can be observed that the range between high and low betas is rather large, suggesting significant volatility. This indicates that an examination into the factors that impact
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fluctuation of betas could be of interest. 3.2 Betas and Trading Volume
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In the second step of the analysis, the Kalman filter betas are used to examine whether
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changes in CAPM betas are associated with trading volume in the precious metals mining sector. Before we conduct a regression analysis between the variables, we follow Gallant et al.
(4)
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by estimating the following equation:
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(1992) and Gebka and Wohar (2013) and adjust trading volume for linear and nonlinear trends
In the rest of the empirical analysis, the residuals ( ) from this regression are used as the
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trading volume variable. We do not report the results of this regression to converse space,
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however, similar to the studies mentioned above, we find that both linear and nonlinear trends are statistically significant and the R-squared of the regressions are approximately 20% on average. We proceed to test for a relation between changes in betas and trading volume for the gold mining stocks by estimating the following model, in which betas calculated as
stands for daily changes in
, by the OLS:
(5)
9
ACCEPTED MANUSCRIPT The regression results are reported in Table 3 and we find that trading volume is indeed a determinant of variation in betas in more than half of the cases in our sample. And a significant
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majority of the statistically significant cases indicate a positive relation between change in betas and trading volume, consistent with the intuition of the study. However, it is important to note
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that the relation is estimated to be negative for three companies in our sample. Furthermore, the coefficients are rather small in each case, which makes it difficult to interpret the economic
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significance of the relation between beta variation and trading volume.
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We also examine whether there is a lagged relation between trading volume and Kalman filter betas. We run the same regression in (5) by including lagged volume as well as
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lagged returns to control for own effects. Information spillover from lagged trading volume to
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betas can exist if the adjustment to new information in the market is gradual rather than instantaneous, which would be consistent with the sequential information arrival model. The
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regression results are reported in Table 4 and we observe that for approximately half of the
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companies in our sample, there is evidence that lagged trading volume is positive and statistically significant.
The OLS analysis conducted above examines the average (mean) relations between the variables. Recent literature, however, shows that the linkages at the extremes, very high/low quantiles, can be different than the mean relations. In other words, trading volume may impact parts of the distribution of the betas other than the means. The quantile regression method is developed by Koenker and Bassett (1978) to capture this intuition by allowing an independent variable to impact a dependent variable at any quantile.
10
ACCEPTED MANUSCRIPT The quantile regression analysis ultimately boils down to an optimization problem. Within the context of the regression model of interest in Equation (5), Koenker and Bassett
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(1978) show that the parameter b can be estimated for any quantile θ (0<θ<1) by minimizing
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the following argument:
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This expression indicates that the method involves the minimization of the sum of asymmetrically weighted absolute error terms (
with different weights for positive and
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negative residuals depending on the quantile chosen (Koenker and Hallock, 2001). The value of b for any θth regression quantile can be estimated by linear programming methods, the simplex
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method is used in the present paper, and standard errors can be bootstrapped.10 We conduct
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the minimization procedure at quantiles of θ=.05, .10, .50, .90 and .95 and thus, obtain quantile specific coefficient estimates. The quantile regression results tend to be useful at the extremes
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of the distributions, which motivates the choice of the specific quantiles used in the paper. In other words, we obtain the relation between beta changes and trading volume at the tails of the distribution of the former, not just the mean as the OLS provides. We first test for contemporaneous relations between daily beta changes and trading volume using the following quantile regression model:
10
Many recent articles apply the quantile regression methodology to financial research, such as Baur and Lucey (2010) and Gebka and Wohar (2013).
11
ACCEPTED MANUSCRIPT (6) is the θ-th quantile of the conditional distribution of
. The results are
T
In which
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reported in Table 3. We now detect that all companies in our sample exhibits a statistically significant relation between changes in beta and trading volume in at least one of the quantiles
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reported. In the higher quantiles of .95 and .90, the relation is largely positive, while more
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negative coefficient estimates are obtained in lower quantiles of .05 and .10. This indicates that there is at least some asymmetry in the trading volume-beta change relation. In other words,
MA
large increases in systematic risk tend to be positively associated with trading volume, which
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has not been reported in the literature before to the best of our knowledge. This further lends support to the argument that trading volume conveys information to
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the market. However, the coefficients continue to be rather small. Moreover, we test whether
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the coefficients are equal across quantiles by means of a Wald test and report the test statistics along with their p-values also in Table 4. This analysis indicates that the null hypothesis of
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coefficient constancy is comfortably rejected in all but two cases, which further illustrates the importance for examining the full distribution of the dependent variable. We also examine whether there are lagged effects from trading volume to beta changes across the quantiles. To accomplish this, we included lagged trading volume, as well as lagged beta changes, in equation (6). The results of this analysis are reported in Table 5. We similarly report Wald tests on parameter constancy across the quantiles examined in this paper. For one third of the companies in the sample, the Wald tests are not statistically significant, which mean the null hypothesis of constant coefficients cannot be rejected. For the companies that 12
ACCEPTED MANUSCRIPT the Wald tests are significant, we find that lagged trading volume has negative covariance with beta changes in the negative tail of the distribution. On the other hand, highly positive beta
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changes are positively correlated with trading volume, similar to the results reported above. 3.3 Returns and Trading Volume
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It could be argued that the dynamic linkage between trading volume and changes in
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betas that is documented above should be observed between trading volume and returns as well if CAPM has empirical validity. Based on this intuition we proceed to examine the volume-
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return linkage of gold mining stocks. In the first part of the empirical analysis, we again examine
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the contemporaneous relation between volume and returns by the OLS and report the findings in Table 6.
PT
We find that returns do not have a statistically significant relation with trading volume,
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save for three companies in our sample. This is consistent with prior work, in which researchers
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generally find that returns do not co-vary with trading volume, see Karpoff (1987) for a survey, and Lee and Rui (2002) and Ciner (2002) for more recent empirical evidence. This is generally regarded as counter to the intuition of financial market practitioners who allude a special role to trading volume and also, to the implications of models by Blume et al. (1994) and Llorente et al. (2001), who show that trading volume can convey important information in markets as mentioned in the Introduction. Similar to the analysis conducted above, we proceed to examine the linkage between trading volume and return by utilizing the quantile regression approach. It is noteworthy that two recent papers also examine the relation between trading volume and returns and utilize 13
ACCEPTED MANUSCRIPT the quantile regression approach. Chuang et al. (2009) uses this technique to show that past trading volume has a positive (negative) effect on returns for the top (bottom) of the return
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distribution for the S&P 500 and FTSE 100 indices. Gebka and Wohar (2013) focus on the Pacific Basin equity markets and find that a very similar picture emerges. Since these studies focus on
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light on whether the findings can be generalized.
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market indexes and aggregate trading volume, our analysis of individual stock returns can shed
We first examine the contemporaneous relation between trading volume and returns by with returns in equation (6) and report the results in Table 6. The Wald test is
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replacing
statistically significant in each case, suggesting quantile dependency in regression coefficients.
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Furthermore, the results are uniform across the sample of companies. Returns in very lower
PT
quantiles (.05 and .10) have a negative relation with trading volume; on the other hand, returns in higher quantiles (.95 and .90) have a positive relation at comfortable statistical significance
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levels. Furthermore, the coefficients estimates are rather large in size, suggesting economic
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significance; however, this is only detected when the conditional quantiles are examined separately highlighting the importance of this method of analysis for this research question. These results are almost identical to those reported by Gebhka and Wohar (2013) and Chuang et al. (2009) by using international stock indices, suggesting the conclusion on volume-return dynamics could be universal. In Table 7, we report the quantile regression results for lagged trading volume. Again, the Wald test is statistically significant in each case. The results also indicate predictive power for trading volume for returns and moreover, the pattern of the findings is similar to those from
14
ACCEPTED MANUSCRIPT lagged volume-beta linkage reported above, which suggests an association between returns and CAPM betas as predicted by the theory. Returns in lower quantiles always have a negative
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relation with lagged volume, while returns in higher quantiles exhibit a positive linkage for each case company in our sample.
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4. Discussion and Concluding Remarks
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As mentioned above, in recent work, Chuang et al. (2009) and Geb kha and Wohar (2013) also investigate volume-return relations in financial markets by relying on stock index
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data. Our results are almost identical to their findings; hence, volume-return relations revealed
ED
by quantile regression seem to be a universal phenomenon in financial markets. Therefore, a discussion of the theoretical underpinnings of the empirically observed volume-return quantile
PT
regression results may be relevant. In particular, while Chuang et al. (2009) suggest that no
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equlibirium model can presently explain the volume-return quantile regression causality empirics, Gebkha and Wohar (2013) forcefully argue that the model by Llorente et al. (2002) is
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consistent with the findings.
Llorenta et al. (2002) build on the work by Wang (1994) and Campbell et al. (1993) to study the role of trading volume in explaining stock return autocorrelations. The underlying intuition of their model is that intensive trading volume occurs either as a result of hedging (portfolio allocation) or speculation (based on private information) by market participants. If hedging is the primary motive to trade, negative return autocorrelations will be observed. That is because investors will sell (buy) at a lower price relative to the fundamental value to accommodate their hedging needs and the price will revert back to the fundamental value in 15
ACCEPTED MANUSCRIPT the next session. However, if speculation is the primary reason to trade, then positive return autocorrelations will be observed. That is because if the underlying private information that
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generated the speculative trade will require more than one period to be fully incorporated into the price.
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Gebka and Wohar (2013) argue that the quartile regression causality results are
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consistent with the above implications. If speculation on positive private information is the primary motive to trade, returns will likely be from higher quantiles today with increased
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trading volume and one should observe a positive relation between volume and returns. A similar implication holds if selling pressure for hedging is the main reason to trade. Hedging
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pressure will generate intensive trading and lower prices today to make the stock attractive for
PT
buyers. However, the stock price will revert back to its fundamental value in the next period generating returns likely from higher quantiles. Thus, a positive relation will be observed
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between trading volume and returns from higher quantiles. If, on the other hand, intensive
AC
trading is due to hedging pressure to buy, next period return will likely be from lower quantiles, since there will be decline in price back to fundamental value. In this case, it is implied that a negative relation between trading volume and returns from lower quantiles will be observed. As the final case, if a low quantile return occurs because of negative private information, similarly negative causality from volume to return will observed since it will take more than one period for the negative information to be incorporated into pricing. Our empirical findings, as well as those of Chuang et al. (2009), are entirely consistent with the implications of tis equilibrium model. Furthermore, our study also shows that the
16
ACCEPTED MANUSCRIPT relation between trading volume and returns is at least somewhat replicated in the linkage between beta and trading volume. This finding lends more support to the role of trading
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volume in financial markets and also suggests that betas and returns are at least somewhat associated, as implied by CAPM for the sample of precious metals firms studied in this article. It
AC
CE
PT
ED
MA
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beta are also valid in other markets and industries.
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would of interest to examine in future research whether the conclusions on trading volume and
17
ACCEPTED MANUSCRIPT References
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Adrian, T., & Franzoni, F. (2009). Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM. Journal of Empirical Finance, 16(4), 537-556.
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Andersen, T. G., Bollerslev, T., Diebold, F. X., & Wu, J. G. (2005). A framework for exploring the macroeconomic determinants of systematic risk (No. w11134). National Bureau of Economic Research.
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Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of applied econometrics, 18(1), 1-22.
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Baur, D. G., & Lucey, B. M. (2010). Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review, 45(2), 217-229.
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Blume, L., Easley, D., & O'hara, M. (1994). Market statistics and technical analysis: The role of volume. The Journal of Finance, 49(1), 153-181.
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Brooks, R. D., Faff, R. W., & McKenzie, M. D. (1998). Time‐varying beta risk of Australian industry portfolios: A comparison of modelling techniques. Australian journal of management, 23(1), 1-22.
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Ciner, C. (2002). Information content of volume: An investigation of Tokyo commodity futures markets. Pacific-Basin Finance Journal, 10(2), 201-215.
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Ciner, C., Gurdgiev, C., & Lucey, B. M. (2013). Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates. International Review of Financial Analysis, 29, 202211. Chuang, C. C., Kuan, C. M., & Lin, H. Y. (2009). Causality in quantiles and dynamic stock return– volume relations. Journal of Banking & Finance, 33(7), 1351-1360. Fabozzi, F. J., & Francis, J. C. (1978). Beta as a random coefficient. Journal of Financial and Quantitative Analysis, 13(01), 101-116. Gallant, A. R., Rossi, P. E., & Tauchen, G. (1992). Stock prices and volume. Review of Financial studies, 5(2), 199-242. Gebka, B., & Wohar, M. E. (2013). Causality between trading volume and returns: Evidence from quantile regressions. International Review of Economics & Finance, 27, 144-159. Karpoff, J. M. (1987). The relation between price changes and trading volume: A survey. Journal of Financial and quantitative Analysis, 22(01), 109-126. 18
ACCEPTED MANUSCRIPT Koenker, R., & Bassett Jr, G. (1978). Regression quantiles. Econometrica: journal of the Econometric Society, 33-50.
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Koenker, R., & Hallock, K. (2001). Quantile regression: An introduction. Journal of Economic Perspectives, 15(4), 43-56. Hiemstra, C., & Jones, J. D. (1994). Testing for Linear and Nonlinear Granger Causality in the Stock Price‐Volume Relation. The Journal of Finance, 49(5), 1639-1664.
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Lee, B. S., & Rui, O. M. (2002). The dynamic relationship between stock returns and trading volume: Domestic and cross-country evidence. Journal of Banking & Finance, 26(1), 51-78.
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Lettau, M., & Ludvigson, S. (2001). Resurrecting the (C) CAPM: A cross‐sectional test when risk premia are time‐varying. Journal of Political Economy, 109(6), 1238-1287.
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Llorente, G., Michaely, R., Saar, G., & Wang, J. (2002). Dynamic volume‐return relation of individual stocks. Review of Financial studies, 15(4), 1005-1047.
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Mergner, S., & Bulla, J. (2008). Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques. The European Journal of Finance, 14(8), 771802.
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Sharpe, W. F., Robichek, A. A., & Cohn, R. A. (1974). The economic determinants of systematic risk. The Journal of Finance, 29(2), 439-447.
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Trecroci, C. (2014). How Do Alphas and Betas Move? Uncertainty, Learning and Time Variation in Risk Loadings*. Oxford Bulletin of Economics and Statistics, 76(2), 257-278.
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ACCEPTED MANUSCRIPT Table 1- Precious Metals Mining Firms
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Data Span 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 11/28/2006- 11/3/2014 5/10/2007- 11/3/2014 7/30/2002- 11/3/2014 9/4/2003- 11/3/2014 1/12/2004- 11/3/2014 7/18/2005- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 1/23/2003= 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 9/14/2006- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/15/2003- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 11/18/2004- 11/3/2014 7/30/2002- 11/3/2014 7/30/2002- 11/3/2014 4/20/2003- 11/3/2014 7/6/2005- 11/3/2014 7/30/2002- 11/3/2014 5/12/2005- 11/3/2014
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Name Barrick Gold Corp. Angle Eagle Mines Ltd. First Majestic Silver Corp. Allied Nevada Gold Corp. AngleGold Ashanti Ltd. AuRico Gold Inc. Yamana Gold Inc. Banro Corp. Buenaventura Gold Corp. Coeur Mining, Inc. Eldorado Gold Corp. Freeport McMoran, Inc. Gold Fields Ltd. Goldcorp, Inc. Rangold Resources Ltd. Gold Resource Corp. Hecla Mining Co. Harmony Gold Mining Co. Iamgold Corp. Kinross Gold Corp. McEwen Mining, Inc. Newmont Mining Corp. New Gold, Inc. Pan American Silver Corp. Royal Gold, Inc. Seabridge God, Inc. Silver Wheaton Corp. Silver Standard Resources, Inc. Tanzanian Royalty Exploration, Inc.
PT CE
AC
Symbol ABX AEM AG ANV AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Note- The data set includes the precious metal mining companies that are included in the Philadelphia Gold and Silver Index.
20
ACCEPTED MANUSCRIPT Table 2- Summary Statistics: Returns
AC
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SC
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Mean Std. Dev. Skewness Kurtosis ABX -.000 .026 .202 7.604 AEM .000 .031 -.551 7.619 AG .000 .043 -.051 2.985 ANV .001 .050 .511 12.502 AU -.000 .029 .515 10.063 AUQ -.000 .039 -.127 3.845 AUY .000 .034 -.167 3.713 BAA -.000 .100 14.372 466.06 BVN .000 .030 -.384 4.767 CDE -.000 .041 -.025 7.176 EGO .000 .036 -.070 6.614 FCX .000 .031 -.477 5.644 GFI -.000 .031 .236 9.116 GG .000 .029 .101 4.883 GOLD .001 .030 .208 4.226 GORO .000 .040 -.034 8.547 HL -.000 .041 -.284 6.504 HMY -.000 .033 .219 5.346 IAG -.000 .033 -.129 5.709 KGC -.000 .032 .033 4.645 MUX .000 .060 1.072 12.535 NEM -.000 .024 .270 6.911 NGD -.000 .043 .949 38.134 PAAS .000 .032 .097 4.851 RGLD .000 .028 -.696 13.549 SA .000 .039 .190 4.589 SLW .000 .036 -.274 4.780 SSRI .000 .037 .039 3.868 TRX .000 .043 .055 7.429 Note- This table provides the descriptive statistics for the returns of the precious metals mining firms included in the data set. Returns are calculated as first differences of logarithms of daily closing stock prices.
21
ACCEPTED MANUSCRIPT
MA ED
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-.09 -.07 .88 .64 .77 .89 .81 .89 1.20 .98 .81
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-.96 -.53 -.70 -1.31 -.51 -.30 -.57 -.46 -.47 -.54 -.53 -.28 -.81 -.74 -.57 -1.43 -.49 -2.68 -.42 -.52 -.26 -.86 -.80 -.02
.63 .02 2.33 .15 .11 .16 .81 -.05 .36 .33 .50 -.04 3.12
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-.10 -.14 .85 -.27 -.15 -.10 -.025 -.16 -.07 -.10 -.02 -.14 1.39
Max. .55 .73
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Min. -1.01 -1.36
CE AC
ABX AEM AG ANV AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Mean -.04 -.47
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Table 3- Summary Statistics: Betas
.31 .58 2.18 1.71 11.36 1.88 2.41 2.21 2.63 2.16 1.67
OLS -.12 -.18 -.19 -.095 -.11 -.15 .79 -.05 -.21 -.17 -.18 -.21 -.094 -.15 -.09 -.16 1.22 -.11 -.22 -.16 .19 .57 .93 .77 .51 .65 1.04 .82 .63
Bai-Perron 18.75 (.00) 18.91 (.00) 6.43 (.50) 9.83 (.15) 15.34 (.01) 25.15 (.00) 31.61 (.00) 53.24 (.00) 16.27 (.00) 17.79 (.00) 50.20 (.00) 11.46 (.08) 24.73 (.00) 19.87 (.00) 36.92 (.00) 53.00 (.00) 90.81 (.00) 8.62 (.24) 38.03 (.00) 31.22 (.00) 625.49 (.00) 73.09 (.00) 18.53 (.00) 66.99 (.00) 47.79 (.00) 36.20 (.00) 47.67 (.00) 105.95 (.00) 32.87 (.00)
Note- This table provides the descriptive statistics for the Kalman filter betas estimated by equations (2)(3) as well as thehe Bai-Perron test for coefficient constancy in equation (1)..
22
ACCEPTED MANUSCRIPT Table 4- Trading Volume and Beta: Contemporaneous Relations
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Median -.000 (.16) .008 (.02) .000 (.06) -.000 (.00) -.000 (.28) -.000 (.02) .000 (.00) .000 (.00) -.000 (.00) .000 (.00) .000 (.00) .000 (.00) .000 (.04) -.000 (.00) .000 (.16) .000 (.00) .000 (.00) -.000 (.21) .000 (.19) -.002 (.26) .001 (.00) .002 (.00) -.000 (.31) -.000 (.94) .002 (.00) .000 (.00)
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OLS -.000 (.74) -.000 (.98) .000 (.24) -.000 (.00) -.000 (.93) -.000 (.41) .000 (.00) .000 (.00) -.000 (.04) .000 (.00) .000 (.00) .000 (.00) .000 (.00) -.000 (.09) -.000 (.12) .000 (.00) .000 (.00) -.000 (.33) .000 (.17) -.002 (.69) .001 (.00) .002 (.00) -.001 (.35) -.001 (.02) .002 (.00) .000 (.00)
NU
.10 -.006 (.00) -.006 (.01) -.004 (.00) -.000 (.00) -.004 (.00) .000 (.00) .001 (.02) .000 (.00) -.000 (.00) .000 (.00) .000 (.00) -.000 (.00) .000 (.75) -.000 (.05) -.006 (.00) -.000 (.00) .000 (.00) .000 (.01) -.001 (.31) -.049 (.00) .002 (.00) .000 (.75) -.001 (.00) -.005 (.00) -.001 (.04) .000 (.03)
ED
.05 -.010 (.00) -.008 (.01) -.007 (.00) -.000 (.00) -.007 (.00) .000 (.60) .000 (.00) .000 (.00) -.001 (.00) .000 (.00) -.000 (.00) -.000 (.00) .000 (.42) .000 (.85) -.009 (.00) -.000 (.00) .000 (.00) .000 (.04) -.002 (.26) -.084 (.00) .003 (.00) .002 (.00) -.001 (.00) -.003 (.31) -.002 (.06) .000 (.02)
CE
AC
ABX AEM AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Wald test 500.98 (.00) 312.87 (.00) 283.19 (.00) 163.74 (.00) 147.32 (.00) 78.77 (.00) 63.41 (.00) 297.82 (.00) 19.25 (.00) 70.89 (.00) 396.50 (.00) 295.32 (.00) 13.43 (.00) 34.53 (.00) 112.33 (.00) 240.94 (.00) 284.92 (.00) 32.31 (.00) 42.10 (.00) 109.74 (.00) 7.41 (.11) 105.04 (.00) 13.34 (.00) 29.19 (.00) 66.91 (.00) 8.86 (.07)
.90 .007 (.00) .006 (.01) .006 (.00) .000 (.00) .003 (.00) -.000 (.00) .000 (.00) -.000 (.00 -.000 (.01) .000 (.00) .000 (.00) .001 (.00) .000 (.00) .000 (.43) .002 (.00) .000 (.24) .001 (.00) -.000 (02) .003 (.00) .041 (.00) .001 (.00) .004 (.00) .001 (.08) -.000 (.78) .005 (.00) .000 (.42)
.95 .010 (.00) .011 (.00) .008 (.00) .000 (.00) .008 (.00) -.000 (.03) .000 (.00) -.000 (.00) -.000 (.98) .000 (.00) .001 (.00) .001 (.00) .000 (.00) -.000 (.27) .000 (.67) .000 (.01) .002 (.00) -.000 (.00) .008 (.00) .059 (.00) .002 (.08) .005 (.08) .000 (.72) .003 (.12) .006 (.08) -.000 (.57)
Note- OLS estimates are from equation (5) and examine the contemporaneous relation between trading volume and the Kalman filter betas. The quantile regression estimates are from equation (6) and test for the contemporaneous relation between the variables at specific quantiles. The p-values are in parentheses. The null hypothesis of the Wald test is equal coefficients across the quantiles.
23
ACCEPTED MANUSCRIPT Table 5- Trading Volume and Beta: Lagged Relations
PT
RI P
T
Median -.000 (.76) -.000 (.40) .000 (.49) .000 (.21) .000 (.63) .000 (.00) .000 (.28) .000 (.70) .000 (.71) .000 (.14) .000 (.38) .000 (.03) .000 (.72) .000 (.82) .000 (.70) .000 (.12) -.000 (.17) .000 (.07) .000 (.35) .000 (.87) .000 (.95) -.000 (.09) -.000 (.73) .000 (.94) -.000 (.67) -.000 (.23)
SC
OLS -.000 (.44) .000 (.86) .000 (.33) -.000 (.00) -.000 (.69) -.000 (.52) .000 (.00) .000 (.00) -.000 (.05) .000 (.00) .000 (.00) .000 (.00) .000 (.00) -.000 (.06) -.000 (.19) .000 (.00) -.000 (.52) .000 (.00) .001 (.08) .001 (.86) .001 (.00) .002 (.00) .000 (.58) -.001 (.11) .002 (.00) .000 (.00)
MA
NU
.10 -.002 (.00) -.002 (.00) -.002 (.00) -.000 (.00) -.001 (.00) -.000 (.57) -.000 (.38) .000 (.35) -.000 (.51) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.05) -.001 (.00) -.000 (.00) -.000 (.04) -.000 (.00) -.002 (.00) -.034 (.00) -.000 (.42) -.000 (.00) -.000 (.00) -.000 (.05) -.000 (.00) -.000 (.45)
ED
.05 -.004 (.00) -.004 (.00) -.003 (.00) -.000 (.00) -.003 (.00) -.000 (.11) -.000 (.15) .000 (.18) .000 (.98) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.00) -.000 (.18) -.003 (.00) -.000 (.00) -.000 (.02) -.000 (.00) -.004 (.00) -.061 (.00) .000 (.97) -.001 (.00) -.000 (.00) -.002 (.00) -.002 (.00) .000 (.33)
CE
AC
ABX AEM AU AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL IAG MUX KGC NEM NGD PAAS RGLD SA SLW SSRI TRX
Wald test 220.67 (.00) 241.99 (.00) 144.42 (.00) 28.32 (.06) 144.61 (.00) 19.03 (.24) 6.00 (.19) 8.23 (.08) 1.79 (.77) 137.28 (.00) 93.15 (.00) 214.98 (.00) 3.20 (.52) 10.61 (.91) 62.88 (.00) 36.54 (.00) 4.99 (.28) 53.41 (.00) 73.91 (.00) 90.85 (.00) 5.24 (.26) 106.34 (.00) 34.74 (.00) 107.27 (.00) 14.12 (.13) 7.87 (.10)
.90 .002 (.00) .002 (.00) .002 (.00) .000 (.00) .001 (.00) .000 (.05) .000 (.04) -.000 (.16) .000 (.41) .000 (.00) .000 (.00) .000 (.00) .000 (.00) .000 (.20) .001 (.00) .000 (.00) -.000 (.37) .000 (.00) .003 (.00) .036 (.00) .000 (.11) .001 (.00) .000 (.00) .001 (.00) .000 (.19) -.000 (.98)
.95 .004 (.00) .004 (.00) .003 (.00) .000 (.00) .003 (.00) .000 (.00) .000 (.02) -.000 (.03) .000 (.33) .000 (.00) .000 (.00) .000 (.00) .000 (.00) .000 (.25) .003 (.00) .000 (.00) -.000 (.38) .000 (.00) .006 (.00) .061 (.00) .000 (.44) .002 (.00) .000 (.00) .003 (.00) .000 (.05) .000 (.43)
Note- OLS estimates are from equation (5) and quantile regression estimates are obtained from equation (6), both obtained by included lagged trading volume in the models. The null hypothesis of the Wald test is equal coefficients across the quantiles.
Table 6- Trading Volume and Returns: Contemporaneous Relations
ABX AEM AG ANV AU
Wald test 800.11 (.00) 864.33 (.00) 164.39 (.00) 69.31 (.00) 823.30 (.00)
.05 -.025 (.00) -.026 (.00) -.015 (.00) -.015 (.04) -.029 (.00)
.10 -.020 (.00) -.023 (.00) -.013 (.00) -.015 (.01) -.023 (.00)
OLS -.000 (.29) -.001 (.15) -.001 (.27) .004 (.09) .000 (.48)
Median .000 (.44) .001 (.31) -.000 (.70) .000 (.21) .000 (.83)
.90 .020 (.00) .024 (.00) .010 (.00) .020 (.00) .023 (.00)
.95 .023 (.00) .030 (.00) .010 (.00) .023 (.00) .029 (.00) 24
ACCEPTED MANUSCRIPT
T
.000 (.68) .000 (.99) -.000 (.00) .001 (.04) .001 (.27) .000 (.99) .001 (.11) .000 (.57) .000 (.63) .000 (.37) .000 (.99) .000 (.99) .001 (.37) .001 (.11) -.000 (.99) .000 (.99) -.000 (.61) .000 (.20) -.000 (.84) -.000 (.69) .003 (.82) .000 (.80) -.000 (.96) -.000 (.99)
SC
RI P
-.000 (.85) -.001 (.29) .004 (.06) -.000 (.91) .001 (.35) .001 (.29) -.003 (.00) .000 (.70) -.001 (.23) .001 (.05) .000 (.92) .000 (.94) -.000 (.82) -.000 (.66) .005 (.00) -.000 (.65) -.001 (.12) -.000 (.97) -.000 (.80) -.001 (.18) .003 (.00) -.001 (.35) -.001 (.40) -.000 (.74)
NU
-.020 (.00) -.017 (.00) -.017 (.00) -.019 (.00) -.022 (.00) -.017 (.00) -.025 (.00) -.018 (.00) -.022 (.00) -.010 (.00) -.017 (.00) -.022 (00) -.024 (.00) -.015 (.00) -.007 (.00) -.022 (.00) -.025 (.00) -.008 (.00) -.021 (.00) -.019(.00) -.014 (.00) -.023 (.00) -.024 (.00) -.019 (.00)
MA
-.030 (.00) -.024 (.00) -.025 (.00) -.023 (.00) -.024 (.00) -.020 (.00) -.034 (.00) -.022 (.00) -.027 (.00) -.011 (.00) -.020 (.00) -.030 (.00) -.028 (.00) -.019 (.00) -.008 (.00) -.026 (.00) -.030 (.00) -.009 (.00) -.027 (.00) -.022 (.00) -.019 (.00) -.028 (.00) -.032 (.00) -.025 (.00)
ED
362.31 (.00) 538.03 (.00) 974.87 (.00) 1148.46 (.00) 300.07 (.00) 241.45 (.00) 502.23 (.00) 481.19 (.00) 863.13 (.00) 217.97 (.00) 434.72 (.00) 381.87 (.00) 513.92 (.00) 459.75 (.00) 174.34 (.00) 388.17 (.00) 1614.20 (.00) 366.79 (.00) 525.51 (.00) 633.68 (.00) 586.38 (.00) 525.60 (.00) 823.03 (.00) 246.92 (.00)
PT
AUQ AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG MUX KGC NEM NGD PAAS RGLD SA SLW SSRI TRX
.022 (.00) .018 (.00) .025 (.00) .021 (.00) .022 (.00) .020 (.00) .020 (.00) .020 (.00) .021 (.00) .011 (.00) .019 (.00) .024 (.00) .024 (.00) .014 (.00) .014 (.00) .022 (.00) .023 (.00) .010 (.00) .021 (.00) .020 (.00) .020 (.00) .022 (.00) .025 (.00) .019 (.00)
.024 (.00) .022 (.00) .032 (.00) .026 (.00) .027 (.00) .022 (.00) .025 (.00) .024 (.00) .027 (.00) .012 (.00) .024 (.00) .032 (.00) .030 (.00) .018 (.00) .016 (.00) .027 (.00) .028 (.00) .013 (.00) .028 (.00) .026 (.00) .024 (.00) .027 (.00) .030 (.00) .025 (.00)
AC
CE
Note- OLS and quantile regression estimates are provided for the relation between returns and trading volume. The p-values are in parentheses. The null hypothesis of the Wald test is equal coefficients across quantiles
Table 7- Trading Volume and Returns: Lagged Relations
ABX AEM AG ANV AU AUQ
Wald test 402.91 (.00) 154.65 (.00) 47.62 (.00) 51.13 (.00) 32.74 (.00) 42.16 (.00)
.05 -.016 (.00) -.031 (.00) -.004 (.01) -.010 (.06) -.012 (.00) -.007 (.03)
.10 -.010 (.00) -.009 (.00) -.003 (.16) .000 (.94) -.008 (.00) -.005 (.00)
OLS -.000 (.53) .000 (.81) -.000 (.59) .000 (.99) .001 (.27) .000 (.99)
Median -.000 (.90) .001 (.15) -.001 (.38) -.000 (.69) .000 (.84) .000 (.59)
.90 .009 (.00) .011 (.00) .003 (.07) -.000 (.80) .008 (.00) .008 (.00)
.95 .012 (.00) .016 (.00) .004 (.09) .000 (.95) .011 (.00) .009 (.00) 25
ACCEPTED MANUSCRIPT
RI P
T
-.000 (.99) -.000 (.99) .001 (.26) .000 (.51) -.000 (.81) .000 (.91) -.001 (.20) -.000 (.88) -.000 (.69) .000 (.99) -.001 (.28) .001 (.35) .000 (.39) -.003 (.02) -.001 (.52) .001 (.34) .000 (.15) -.001 (.26) -.002 (.06) .001 (.21) .001 (.86) -.001 (.30) -.000 (.79)
SC
-.001 (.10) .004 (.06) .000 (.39) .000 (.76) -.001 (.23) .000 (.51) -.001 (.13) -.000 (.43) -.000 (.89) .002 (.08) -.000 (.89) -.000 (.86) -.000 (.59) -.002 (.03) -.001 (.10) -.000 (.99) .001 (.15) -.003 (.02) -.002 (.08) .002 (.01) -.000 (.86) -.003 (.02) -.000 (.97)
NU
-..009 (.00) -.009 (.02) -.009 (.00) -.007 (.02) -.003 (.05) -.014 (.00) -.012 (.00) -.010 (.00) -.005 (.00) -.002 (.34) -.010 (.00) -.009 (.00) -.008 (.00) -.001 (.00) -.003 (.05) -.006 (.00) -.005 (.00) -.007 (.00) -.009 (.00) -.003 (.04) -.012 (.00) -.012 (.00) -.010 (.00)
MA
-.012 (.00) -.019 (.00) -.009 (.00) -.009 (.00) -.004 (.10) -.012 (.00) -.013 (.00) -.015 (.00) -.007 (.00) .001 (.65) -.021 (.03) -.013 (.00) -.001 (.00) -.014 (.00) -.005 (.00) -.013 (.00) -.008 (.00) -.008 (.00) -.010 (.00) -.006 (.00) -.021 (.00) -.014 (.00) -.011 (.00)
ED
117.56 (.00) 69.13 (.00) 57.70 (.00) 337.47 (.00) 19.17 (,00) 67.23 (.00) 300.55 (.00) 311.75 (.00) 12.67 (.01) 48.84 (.01) 121.31 (.00) 128.13 (.00) 214.12 (.00) 347.44 (.00) 32.45 (.00) 25.02 (.00) 92.32 (.00) 4.07 (.04) 82.06 (.00) 10.88 (.02) 30.44 (.03) 85.07 (.00) 10.38 (.03)
.006 (.00 .015 (.00) .009 (.00) .003 (.14) -.000 (.75) .012 (.00) .007 (.01) .007 (.00) .006 (.00) .004 (.08) .006 (.00) .009 (.00) .004 (.02) .004 (.01) .000 (.76) .004 (.04) .006 (.00) .001 (.57) .007 (.00) .009 (.00) .006 (.01) .001 (.48) .008 (.00)
.007 (.00) .025 (.00) .016 (.00) .003 (.28) -.002 (.35) .017 (.00) .009 (.00) .011 (.00) .008 (.00) .008 (.03) .010 (.00) .013 (.00) .007 (.01) .008 (.00) -.003 (.40) .008 (.00) .010 (.00) -.001 (.64) .008 (.00) .011 (.00) .010 (.00) .005 (.09) .013 (.00)
PT
AUY BAA BVN CDE EGO FCX GFI GG GOLD GORO HL HMY IAG KGC MUX NEM NGD PAAS RGLD SA SLW SSRI TRX
Note- OLS and quantile regression estimates are provided in this table for the predictive power of
AC
CE
lagged trading volume for returns. The p-values are in parentheses. The null hypothesis of the Wald test is equal coefficients across quantiles.
26
ACCEPTED MANUSCRIPT Highlights
T
RI P
SC NU MA ED PT
-
CE
-
Explanatory power of trading volume is examined for both time varying CAPM betas and stock returns for the precious metals mining sector Quantile regressions indicate asymmetric dynamics between the variables Returns from higher (lower) quantiles have a positive (negative) linkage with both contemporaneous and lagged trading volume Results on volume-return relation is consistent with equilibrium models on return autocorrelations
AC
-
27