Trading Volume, Volatility and ADR Returns

Transcription

1 Trading Volume, Volatility and ADR Returns Priti Verma, College of Business Administration, Texas A&M University, Kingsville, USA ABSTRACT Based on the mixture of distributions hypothesis (MDH), this paper examines the relationship between trading volume and American Depositary Receipt (ADRs) returns. We investigate the GARCH cum volume models to examine whether trading volume can be identified as a mixing variable for the rate of daily information for ADRs. Results show that when trading volume is included in the conditional variance equation, the volatility persistence decreases marginally but not substantially in all the ADRs from Latin America, Asia and Europe. These results are not consistent with the findings of those from the developed markets. Future research should focus on the causes and modeling of the ADR volatility. JEL classification codes: C3, G10, G15 Keywords: ADRs, GARCH, Trading volume, Volatility INTRODUCTION The autoregressive conditionally heteroscedastic (ARCH) process of Engle (198) has been shown to provide a good fit for many time series data. ARCH imposes an autoregressive structure on the conditional variance and allows the volatility shocks to persist over time. One of the possible explanations for the ARCH effect is based on the hypothesis that a mixture of distributions generates daily returns (Clark 1973; Epps and Epps, 1976). Further, the rate of daily information arrival is the stochastic mixing variable. According to the mixture of distributions hypothesis (MDH), the ARCH effect in stock returns is explained by a serially correlated mixing variable that measures the rate of daily information arrival (Clark 1973; Epps and Epps, 1976; Tauchen and Pitts, 1983; Harris, 1987). Theoretical explanations to the MDH were initially advanced by Clark (1973), Epps and Epps (1976), Tauchen and Pitts (1983), Harris (1987) and Lamoureux and Lastrapes (1990, 1994). The MDH has been extensively documented for developed markets like the U.S stock market (Lamoureux and Lastrapes, 1990; Kim & Kon, 1994; Andersen, 1996; Gallo & Pacini, 000) and the U.K. market (Omran and McKenzie, 000). In general, results in the developed markets support the MDH. Evidence shows that inclusion of trading volume (a proxy for rate of information arrival) in the conditional variance equation, results in a substantial decrease in the volatility persistence and sometimes causes it to disappear. MDH has also been documented for the developing markets and has found contradictory evidence. Brailsford (1996) and Pyun et al. (000) investigate the effect of information arrival on volatility persistence in the Australian and Korean stock exchange respectively and find evidence in favor of MDH. Bohl and Henke (003) examine the same for 0 Polish stocks and finds mixed evidence. Ahmed et. al. (005) examine MDH in the Malaysian stock markets and find that volatility persistence remains and does not decrease. In majority of cases the volatility persistence disappears when trading volume is included in the conditional variance equation but MDH is not conformable in all the cases. The Journal of Global Business Management Volume 11* Number * October 015 Issue 3

2 Overall, the extant literature provides support for the return-volume relationship in the developed and mixed evidence in developing country stock markets. However, this relationship has been little understood for American Depositary Receipts (ADRs). ADRs are U.S. dollar-denominated negotiable receipts that represent shares of foreign companies, which list and trade in U.S. stock markets. The ADR market has been rapidly expanding to meet the growing demand of U.S. investors in their pursuit for international diversification. This paper provides additional evidence on the relationship between the trading volume and the time-varying conditional heteroscedasticity of stock returns by testing the validity of MDH in the ADR markets. Specifically, this paper tests whether trading volume can be identified as an explanatory mixing variable for the rate of daily information arrival in the ADR markets. This paper contributes to the existing literature in two ways. First, it examines the validity of MDH in ADRs. Particularly, this paper examines whether trading volume can be identified as a mixing variable for the rate of daily information for ADRs. Second, whether ADR markets parallel the evidence that is found in the developed markets or the developing markets. Using daily data and following Lamoureux and Lastrapes (1990), this paper investigates the GARCH cum volume models for daily ADR returns. The results indicate that when trading volume is included in the conditional variance equation, the volatility persistence decreases marginally but not substantially in all the ADRs. These results are not consistent with the findings of the developed markets and tend to mimic the developing markets. Since the testable implications of MDH are not conformable, future research on all the causes of volatility is essential. The balance of the paper is structured as follows: Section highlights the econometric methodology while Section 3 discusses the data and Section 4 the empirical results, followed by the concluding remarks in Section 4. ECONOMETRIC METHODOLOGY One of the many possible explanations for the ARCH effect is based on the hypothesis that stock returns are generated by a mixture of distributions. The theoretical explanation used to explain MDH was developed by Clarke (1973) and extended by Tauchen and Pitts (1983). Further, we follow the specification used by Lamoureux and Lastrapes (1990) in his paper. Let y t be the continuously compounded return over a full trading day on a financial asset. Then y t is equal to the sum of i = 1,,..n t intraday equilibrium returns, δ it. n t yt it (1) i 1 where n t is the integer random variable that represents the number of information arrivals to the market on day t. Each is independently and identically distributed with mean zero and variance. it In the above n t is the stochastic mixing variable and governs the rate of information arrivals of. This in turn determines the daily return y t. If the intraday equilibrium returns it are independently and identically distributed and the number of information arrivals n t is sufficiently large, then according to central limit theorem, n y / n ~ N(0, t ) () t t The above equation shows that the daily returns conditional on the number of information arrivals are normally distributed with zero variance and a variance term. Further, the variable n t is unknown and it 4 The Journal of Global Business Management Volume 11* Number * October 015 Issue

3 therefore proxies for it have to be chosen. In general, trading volume is the proxy that empirical studies use to approximate information flows (Andersen, 1996; Lamoureux and Lastrapes, 1990). Furthermore, it is assumed that the number of information arrivals follows an autoregressive process: n (L)n u (3) t 0 1 t 1 t where t t t (L) is the lag polynomial and u 1 t is the white noise error term. Also, defining E( n ) and if the model is valid then n. Substituting equation (3) in to the variance t equation gives us: (L) u (4) t 1 t 1 t Furthermore, this paper investigates the GARCH(1,1) cum volume model for daily returns: y (5) t 0 1yt 1 t h h V (6) t 0 1 t 1 t 1 3 t where y t are the stock returns measured as log P t logp t-1, where P t is the value of the index at time t and V t is the trading volume series. Firstly, this paper estimates a restricted version of equation (6) by setting 3 0. The volatility persistence is measured by the sum of ( 1 ). As this sum approaches unity, greater is the persistence of shocks to volatility. Secondly, this paper estimates the unrestricted version of equation (6) and determine the volatility persistence. If the trading volume is serially correlated the persistence of volatility measured by ( 1 ) reduces considerable and in some cases disappears. However, an essential condition for the above to hold is the presence of serial correlation in the trading volume series. This is because MDH implies that the presence of serial correlation in the trading volume series causes the conditional heteroscedasticity in stock returns. The serial correlation for the trading volume series is analyzed by using the Philips-Perron (1988) unit root tests. t DATA ADRs provide one avenue for investors to diversify internationally while eliminating the hassles and transaction costs of direct investments in foreign stock markets since they are denominated in and traded in U.S. dollars. At the end of 004, the trading volume of ADRs on the New York Stock Exchange (NYSE), American Stock Exchange (AMEX), and Nasdaq reached a record high of 39.1 billion shares (an increase of 18% over 003) valued at $885 billion (an increase of 40% over 003).( To investigate the mixture of distribution hypothesis for ADRs, this paper considers six emerging stock markets from Latin America (Argentina, Brazil, Chile, Columbia, Mexico, and Venezuela), six from Asia (China, Japan, Korea, Taiwan, Philippines, and Singapore) and six from Europe (Germany, France, Italy, U.K., Switzerland, and Finland). All data are obtained from the DataStream International database. The data used in this study are the daily closing equity prices of the ADR country indexes provided by the Bank of New York (BNY) Mellon. ( The BNY Mellon indexes track all the ADRs traded on the NYSE, AMEX and Nasdaq and are calculated on a continuous basis throughout the trading day. All these indexes are value-weighted and are adjusted for free-float using the same method used in calculating the Dow Jones indices. The data set covers the period June 1, 000 to December 31, 003 and contains 935 observations. Daily percentage returns are calculated as log P t logp t-1, where P t is the end of the day closing price of the ADR index. This paper uses the daily data series for this study since The Journal of Global Business Management Volume 11* Number * October 015 Issue 5

4 weekly returns may be too long to examine the rapid interactions between stock markets (Eun and Shim, 1989; Chowdhry, 1994). Table 1 reports the summary statistics for the daily returns series for each country. All the series have excess kurtosis which shows that they are more peaked and have fat tails than normal distribution. Further, a significant Jarque-Bera test statistics also shows that the each of the series again is not normally distributed. This is mainly caused by excess kurtosis, indicating that short term returns are characterized more by fat tails than by asymmetry. Clearly, these descriptive statistics indicate that these data fit the ARCH type modeling approach employed in this study. Table 1: Descriptive Statistics of Returns of the ADRs ADRs Mean Std. Dev. Excess- Median Maximum Minimum Skewness (%) (%) Kurtosis Jarque-Bera Argentina (0.0000)*** Brazil (0.0000)*** Chile (0.0000)*** Columbia (0.0000)*** Mexico (0.0000)*** Venezuela (0.0000)*** Germany (0.0000)*** France (0.0000)*** Italy (0.0000)*** U.K (0.0000)*** Switzerland (0.0000)*** Finland (0.0000)*** China (0.0000)*** Japan (0.0000)*** Korea (0.0000)*** Taiwan (0.0000)*** Philippines (0.0000)*** Singapore (0.0000)*** This table displays the descriptive statistics of ADR returns. The sample spans the period from June 1, 000 to December 31, 003 and contains 935 observations. Daily percentage returns are calculated as 100 (log P t log P t-1), where P t is the value of the index at time t in terms of the local currency. The Jarque-Bera statistic tests the null hypothesis of normality. *** denotes statistical significance at the 1% levels. Table reports the Ljung-Box Q statistics for the individual volume series for up to 1 lags. This test is performed to test the presence of serial correlation. All the trading volume series exhibit serial correlation and all the Ljung-Box statistics are significant at 1% level. Therefore, for all the 18 ADR indexes, the rate of information measured by trading volume is serially correlated. The presence of serial correlation in a volume series is essential in implementing the mixture of distributions hypothesis (MDH) with GARCH specifications. This is because it is hypothesized that in MDH the presence of serial correlation in volume data causes the conditional heteroscedasticity of stock returns data. 6 The Journal of Global Business Management Volume 11* Number * October 015 Issue

5 ADRs Table : Serial Correlation of the daily volume series of ADRs Number of lag length for serial correlation Argentina Brazil Chile Columbia Mexico Venezuela Germany France Italy U.K Switzerland Finland China Number of lag length for serial correlation ADRs Japan Korea Taiwan Philippines Singapore This table displays the serial correlation of the daily volume series of ADRs returns. The sample spans the period from June 1, 000 to December 31, 003 and contains 935 observations. Autocorrelation coefficients contain upto 1 lags and the Ljung Box Q statistics are shown in parenthesis. Philips-Perron (1988) unit root tests are performed on the individual volume series for all the ADR country indexes. If the volume series is nonstationary then subsequent tests for the effect of volume on the conditional variance may not be valid. Table 3 reports the results of the Philips-Perron unit root tests. Results indicate that all the volume series are stationary with or without the presence of a deterministic trend in the level of each volume series. The Philips-Perron test is preferred over unit root tests suggested by Dickey and Fuller (1981) as this test is robust to the presence of serial correlation and heteroscedasticity. The Journal of Global Business Management Volume 11* Number * October 015 Issue 7

6 Table 3: Phillps-Perron unit root tests for the daily volume series of ADRs ADRs Without Trend With Trend Argentina Brazil Chile Columbia Mexico Venezuela Germany France Italy U.K Switzerland Finland China Japan Korea Taiwan Philippines Singapore Test Critical Values 1% level % level % level This table displays the Phillips-Perron unit root tests for the daily volume series of ADRs. The sample spans the period from June 1, 000 to December 31, 003 and contains 935 observations. The reported numbers are the Phillips-Perron t-statistics. DISCUSSION OF RESULTS If MDH can explain the ARCH effect in the ADR returns, then the volume series, which is a proxy for the rate of arrival of information, absorbs the volatility persistence in the conditional variance process of GARCH (1, 1). In case the volatility persistence does not decrease with the inclusion of the volume series in the conditional variance equation, then MDH does not explain the ARCH effect in the ADR returns. Table 4 presents the results of the estimated GARCH (1, 1) model. The second and third columns represent the parameters of the ARCH term and the GARCH term respectively, in the conditional equation. The sum of the ARCH and the GARCH term measures the persistence of volatility of the conditional variance series. The fourth column represents the sum of these two parameters in the GARCH (1, 1) model. In majority of the cases the sum is close to 0.90 which indicates that the return series has high persistence in the volatility of the ADRs. Further, all the coefficients are statistically significant at 1% level. The findings are consistent with the findings of Gallo and Pacini (000), Omran and McKenzie (000), Kim and Kon (1994) and Lamoureux and Lastrapes (1990) who find a high degree of volatility persistence for the U.S and the U.K. stocks. 8 The Journal of Global Business Management Volume 11* Number * October 015 Issue

7 Table 4: Maximum Likelihood Estimation of ADRs using GARCH (1,1) β 1 β β 1 + β Argentina (0.0000)*** (0.0000)*** Brazil (0.0000)*** (0.0000)*** Chile (0.0000)*** (0.0000)*** Columbia (0.0000)*** (0.0000)*** Mexico (0.0000)*** (0.0000)*** Venezuela (0.0000)*** (0.0000)*** Germany (0.0000)*** (0.0000)*** France (0.0000)*** (0.0000)*** Italy (0.0000)*** (0.0000)*** U.K (0.0000)*** (0.0000)*** Switzerland (0.0000)*** (0.0000)*** Finland (0.0000)*** (0.0000)*** China (0.0000)*** (0.0000)*** Japan (0.0000)*** (0.0000)*** Korea (0.0000)*** (0.0000)*** Taiwan (0.0000)*** (0.0000)*** Philippines (0.0000)*** (0.0000)*** Singapore (0.0000)*** (0.0000)*** This table displays the maximum likelihood estimation of ADRs using GARCH (1, 1). The sample spans the period from June 1, 000 to December 31, 003 and contains 935 observations. The GARCH (1, 1) model is estimated based on Eqs. (1)-(): yt y and. h h *** denotes statistical significance at the 1% levels. 0 1 t 1 t t 0 1 t 1 t 1 Table 5 presents the results of the GARCH (1, 1) cum volume model. The second and third columns represent the parameters of the ARCH term and the GARCH term respectively, in the conditional equation. The fourth column represents the parameter estimates of the trading volume in the variance equation. The sum of the ARCH and GARCH term is presented in the last column. For all the stocks, volatility persistence has reduced marginally but not very much. Also, for majority of the all the ADR return series the volume effect is statistically significant at 1% level. This implies that when trading volume is added in the variance equation, the degree of persistence reduces slightly and not substantially. This indicates that the rate of information arrival which is measured by the volume series is not a source of conditional heteroscedasticity in the ADR returns. Table 5: Maximum Likelihood Estimation of ADRs using GARCH (1,1) cum volume models β 1 β β 3 β 1 + β Argentina (0.0000)*** (0.0000)*** (0.0000)*** Brazil (0.0000)*** (0.0000)*** (0.179) Chile (0.0000)*** (0.0000)*** (0.0000)*** Columbia (0.0000)*** (0.0000)*** (0.0000)*** Mexico (0.0000)*** (0.0000)*** (0.0013)*** Venezuela (0.0000)*** (0.0000)*** (0.0000)*** Germany (0.0000)*** (0.0000)*** (0.0000)*** France (0.0000)*** (0.0000)*** (0.559) Italy (0.0000)*** (0.0000)*** (0.0804)** U.K (0.0000)*** (0.0000)*** (0.0199)* Switzerland (0.0000)*** (0.0000)*** (0.0000)*** Finland (0.0000)*** (0.0000)*** (0.0000)*** China (0.0000)*** (0.0000)*** (0.051)** Japan (0.0000)*** (0.165) (0.0000)*** Korea (0.0000)*** (0.0000)*** (0.0934)** The Journal of Global Business Management Volume 11* Number * October 015 Issue 9

8 Taiwan (0.0000)*** (0.0000)*** (0.0000)*** Philippines (0.0000)*** (0.0000)*** (0.0000)*** Singapore (0.0000)*** (0.0175)* (0.0000)*** This table displays the maximum likelihood estimation of ADRs using GARCH (1, 1) cum volume models. The sample spans the period from June 1, 000 to December 31, 003 and contains 935 observations. The GARCH (1, 1) cum volume model is estimated based on Eqs. (1)-(): yt 0 1yt 1 t and, ht 0 1 t 1 ht 1 3Vt where V t is the trading volume series. ***, **, * denotes statistical significance at the 1%, 5% and 10% levels respectively. The ADR returns are not unanimously favorable for the testable implications of MDH. When trading volume is included in the return-volume relationship for the U.S. and U.K. stocks, the degree of persistence substantially reduces for all the stocks under investigation. The evidence by Pyun et. al. (000) also shows a reduction in volatility persistence for Korean stocks. CONCLUDING REMARKS An explanation for ARCH effects in stock returns is based on the fact that daily stock returns are generated by a stochastic mixing variable which measure the rate of daily information arrivals to the market. Further, trading volume can be a proxy for rate of daily information arrival. The return-volume relationship has been well documented for developed stock markets like the U.S. and the U.K. However, this is yet to be extended to the field of ADRs. This paper attempts to provide additional evidence on the relationship between the trading volume and the time-varying conditional heteroscedasticity of ADR returns by testing the validity of MDH in the ADR markets. We examine the return-volume relationships for 18 ADRs to determine whether MDH can explain the ARCH effect in the ADR returns. Results show that when trading volume is included in the conditional variance equation of all the 18 country ADRs, the volatility persistence decreases marginally but not substantially. We conclude that volume series is not a source of conditional heteroscedasticity in the ADR returns and that MDH is not relevant in explaining the ARCH effect in the ADR markets. The findings of this study have important implications for finance as these estimated variances are used as risk measures and directly enter the Black-Scholes model of options pricing. Further, heteroscedasticity must be taken into account for testing for market efficiency. While research has found substantial evidence of MDH in the developed stock markets, the inclusion of trading volume does not significantly decrease volatility persistence in case of ADRs. This encourages future research on the ADR market. The extent of future research may be given by the fact of investigating alternate proxies for measuring the rate of information arrival in the ADR market. Further, extensions of GARCH models could be applied to include asymmetries and effects of price regulation. REFERENCES Ahmed, H. J., Ali Hassan, and A. Nasir., (005). The relationship between trading volume, volatility and stock market returns: A test of Mixed Distribution Hypothesis for a Pre and Post crisis on Kuala Lumpur Stock Exchange, Investment management and financial innovations (005): Andersen, (1996). Return volatility and trading volume: An information flow interpretation of stochastic volatility, Journal of Finance, 51, Brailsford, (1996) The empirical relationship between trading volume, returns, and volatility, Accounting and Finance, 35, The Journal of Global Business Management Volume 11* Number * October 015 Issue

9 Bohl, M.T., and Henke, H. (003). Trading Volume and stock market volatility: The Polish Case, International Review of Financial Analysis, 1, Choudhry T., (1994). Interdependence of stock markets: Evidence from the Asian NIE s. Journal of Macroeconomics 16, Clark, (1973). A subordinated stochastic process model with finite variance for speculative prices. Econometrica, 41, Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, Epps, W. and Epps, M. (1976). The stochastic dependence of security price changes and transaction volumes: Implications for the mixture of distributions hypothesis, Econometrica, 44, Eun, S.C., and S. Shim, (1989). The international transmission of stock markets movements. Journal of Financial and Quantitative Analysis 4, Gallo, G. and Pacini, B. (000). The effects of trading activity on market volatility, European Journal of Finance, 6, Harris, L., (1987). Transaction data tests of the mixture of distributions hypothesis, Journal of Financial and Quantitative Analysis,, Kim D. and Kon, S. (1994). Alternative models for the conditional heteroscedasticity of stock returns, Journal of Business, 67, Lamoureux, C. and Lastrapes, L. (1990). Heteroscedasticity in stock return data: Volume versus GARCH effects, Journal of Finance, 45, 1 9. Lamoureux, C.G. and Lastrapes, W.D., (1994). Endogenous trading volume and momentum in stock-return volatility Journal of Business and Economic Statistics, 1, Ljung, G. and Box, G. (1978). On a measure of lack of fit in time series models, Biometrika, 66, Omran, M. and McKenzie, E. (000). Heteroscedasticity in stock returns data revisited: Volume versus GARCH effects, Applied Financial Economics, 10, Phillips, P. and Perron, P., (1988). Testing for a unit root in time series regression, Biometrica, 75, Pyun, C. Lee, S. and Nam, K. (000). Volatility and information flows in emerging equity markets: A case of the Korean stock exchange, International Review of Financial Analysis, 9, Tauchen, G. and Pitts, M. (1983). The price variability volume relationship on speculative markets, Econometrica, 51, The Journal of Global Business Management Volume 11* Number * October 015 Issue 31