The bivariate GARCH approach to investigating the relation between stock returns, trading volume, and return volatility

Abstract

We use a bivariate GJR-GARCH model to investigate simultaneously the contemporaneous and causal relations between trading volume and stock returns and the causal relation between trading volume and return volatility in a one-step estimation procedure, which leads to the more efficient estimates and is more consistent with finance theory. We apply our approach to ten Asian stock markets: Hong Kong, Japan, Korea, Singapore, Taiwan, China, Indonesia, Malaysia, the Philippines, and Thailand. Our major findings are as follows. First, the contemporaneous relation between stock returns and trading volume and the causal relation from stock returns and trading volume are significant and robust across all sample stock markets. Second, there is a positive bi-directional causality between stock returns and trading volume in Taiwan and China and that between trading volume and return volatility in Japan, Korea, Singapore, and Taiwan. Third, there exists a positive contemporaneous relation between trading volume and return volatility in Hong Kong, Korea, Singapore, China, Indonesia, and Thailand, but a negative one in Japan and Taiwan. Fourth, we find a significant asymmetric effect on return and volume volatilities in all sample countries and in Korea and Thailand, respectively.

Introduction

From a theoretical and practical standpoint, stock returns, trading volume, and return volatility are jointly and simultaneously determined by the same market dynamics, and are inextricably linked. Prior empirical studies, however, have seldom analyzed stock returns, return volatility and trading volume as a joint system. A partial estimation of the system can hide the true dynamics and lead to inefficient and potentially biased estimations. Many studies have relied on a two-step procedure to avoid the joint estimation of the system. This two-step process may suffer from a generated regressor problem—see Pagan (1984).¹ A related empirical issue in the prior literature regards the dynamics of trading volume. Trading volume may also exhibit a time varying variance as stock returns. Consequently, the usual OLS estimates of trading volume may be inefficient.²

In this paper, we use a bivariate system of equations to estimate the dynamic behavior of stock returns and trading volume. To this end, we specify the conditional mean equations of stock returns and trading volume as a Vector Autoregression (VAR), which allows us to examine the causal relation between stock returns and trading volume. The contemporaneous relation between these two variables is gaged through the conditional contemporaneous correlation coefficient of the model. To introduce into our VAR model return volatility dynamics, we use a bivariate GARCH model, and thus, we incorporate trading volume–return volatility interrelations into the system. The lagged squared residuals of stock returns, endogenously generated from the model, are incorporated into the conditional mean equation of trading volume to measure the causal relation from return volatility to trading volume. Lagged trading volume is added into the conditional variance equation of stock returns to measure the causal relation from trading volume to return volatility.

Our model specification has three advantages. First, and most importantly, it investigates simultaneously these relations in a one-step estimation procedure, leading to the more efficient estimates. In addition, the simultaneous estimation is more consistent with finance theory, where stock returns, trading volume, and return volatility are jointly and simultaneously determined by the same market dynamics. Second, our GARCH formulation allows us to examine asymmetric effects of positive and negative innovations on both return and volume volatilities.³ Third, the more precise measures of the causal relations help investors to predict future stock market movements and the degree of risk and liquidity to develop their trading strategies and firms to make decisions about their corporate strategies.⁴ For example, a better forecast of market liquidity can be obtained conditioning on information embedded in stock returns and return volatility, instead of conditioning on only either one.

We apply our model to ten Asian stock markets: Hong Kong, Japan, Korea, Singapore, Taiwan, China, Indonesia, Malaysia, the Philippines, and Thailand.⁵ We choose these markets for two reasons. First, Griffin et al. (2007) argue that the return- and volatility–volume relations should be stronger in less efficient markets such as emerging markets, where presumably information is incorporated in price more sluggishly. With the exception of the first five stock markets, which we use as a benchmark, the Asian stock markets have been widely recognized as emerging markets in the literature—see Richards (2005) and Edison and Warnock (2008).⁶ Second, most empirical studies have focused on the U.S. stock markets, but relatively little work has been conducted on the Asian stock markets. Our study attempts to remedy this situation.

Our major findings are as follows. First, we find that the contemporaneous relation between stock returns and trading volume and the causal relation between lagged stock returns and current trading volume are statistically significant and robust across all sample stock markets. Second, we find a positive bi-directional causality between stock returns and trading volume only in Taiwan and China. A positive bi-directional causality between trading volume and return volatility is found in Japan, Korea, Singapore, and Taiwan. Third, we find a positive contemporaneous relation between trading volume and return volatility in Hong Kong, Korea, Singapore, China, Indonesia, and Thailand, but a negative one in Japan and Taiwan. Fourth, we find a significant asymmetric effect on stock return volatility in all markets and on volume volatility only in Korea and Thailand.

The remainder of the article is organized as follows. Section 2 provides a brief overview of the literature on the contemporaneous and causal relations between stock returns and trading volume and between trading volume and return volatility. Section 3 introduces the data, describes the method to filter trading volume series to achieve stationarity, and reports some important descriptive statistics on the data. Section 4 discusses our model specification. Section 5 presents and discusses the empirical results. Section 6 concludes the paper.