Asian Review of Financial Research Vol.32 No.2 pp.149-186
Mean Reversion of the Trading Volume
Key Words : Trading Volume,Mean Reversion,Autocorrelation,Unit Root Test,Korean Stock Market
This study analyzes the mean reversion of trading volume, which allows us to predict future trading volumes from time-series data. The results have important implications for various related concerns, including the predictability of returns in relation to trading volumes, liquidity, and the use of practical indicators such as the VWAP (volume-weighted average price) and the CGO (capital gains overhang). We test the trading volumes of the indices, size-portfolios, and individual stocks on the Korean stock market from 1999 to 2017. All of the sample data are obtained from FnDataGuide. First, we test the autocorrelation of the trading volume. The results show that the trading volume has a positive autocorrelation, and that changes in trading volume have negative autocorrelations. Therefore, we confirm that the trading volume process (unlike the return process) does not follow an independent distribution. As mean reversion implies a correlated time-series, the autocorrelation of trading volumes serves as the premise for the mean reversion of trading volumes. Next, we use the Phillips-Perron test (Phillips and Perron, 1988) and the KPSS test (Kwiatkowski, Phillips, Schmidt, and Shin, 1992) to verify the mean reversion property of the trading volume. The results show that the trading volume of the indices, size-portfolios, and 96% of the individual stocks, all have a mean reversion property on the Korean stock market. In addition, we calculate the mean-reverting speed for each stock by applying the Ornstein–Uhlenbeck model (Uhlenbeck and Ornstein, 1930) to identify the variables that affect the mean reversion property of the trading volume. We regard the mean-reverting speed as a proxy variable that indicates the relative strength of the mean reversion property across sample stocks. This analysis of the mean-reverting speed enables us to confirm which variables affect the mean reversion of the trading volume. Before the regression analysis, we compare the actual mean-reverting duration of the trading volume with the duration calculated by using the Ornstein-Uhlenbeck model, which is our model for estimating the mean-reverting duration of the trading volume. As the implied error of the model has an acceptable scale, we confirm that our Ornstein-Uhlenbeck model can serve as a reasonable model for trading volume. The regression results on the mean-reverting speed of each stock shows that the smaller the size, the smaller the stock price volatility. In addition, we find that the smaller the ratio of the individual investors' trading activity and the higher the number of analysts' reports, the higher the mean-reverting speed. This set of findings suggests that the mean reversion of the trading volume can be explained by the presence of stealth trading (Kyle, 1985; Admati and Pfleiderer, 1988; Foster and Viswanathan, 1990; Wang, 1994) and by individual investors' attention-based trading (Barber and Odean, 2008). Heterogeneity between investors generates trading volume. This heterogeneity is resolved by opinion-sharing with trades. However, stealth trading by informed investors delays the incorporation of information, and attention-based trading by individual investors gives the trading volume a positive feedback. Thus, the mean-reverting speed of a stock is slower in trading environments where it is easier to hide information, and where individual investors trade more actively. Additionally, we show that the future trading volume can be estimated from its mean-reversion property. If we know the mean-reverting speed, the mean value, and the standard deviation of the trading volume, we can obtain the expected trading volume by applying the Ornstein-Uhlenbeck model. This study contributes to the literature in the following four ways. First, and most importantly, it expands research on trading volumes by demonstrating that the volume has a mean reversion property on the Korean stock market. Understanding this property takes us one step beyond making predictions based on the autocorrelation of the trading volume. Second, we find that the future trading volume can be predicted by its mean reversion property. This novel finding helps to expand the knowledge of market dynamics among academics, and it can help practitioners who want to build their positions without causing a serious market impact. Third, we show that the trading volume has a positive autocorrelation in the Korean stock market. Although such autocorrelation of trading volume has been previously studied in the U.S. stock market, it has not been investigated in the Korean stock market. As the scope for applying autocorrelation is wide, we believe that the verification of autocorrelation is also important. Last, we shed light on why the trading volume shows mean-reversion properties. We assess trade sizes, price volatility, the trading activity of individual investors, and the number of analysts' earnings estimates, all of which influence the mean reversion of the trading volume. All of these factors can be partly explained by stealth trading and the attention-based trading of individual investors.