Equity Trading Volume and Volatility: Latent Information Arrivals and Common Long-Run Dependencies

Tim Bollerslev, Dan Jubinski
1999 Journal of business & economic statistics  
This article examines the behavior of equity trading volume and volatility for the individual firms composing the Standard & Poor's 100 composite index. Using multivariate spectral methods, we find that fractionally integrated processes best describe the long-run temporal dependencies in both series. Consistent with a stylized mixture-of-distributions hypothesis model in which the aggregate "news"-arrival process possesses long-memory characteristics, the long-run hyperbolic decay rates appear
more » ... decay rates appear to be common across each volume-volatility pair. KEY WORDS: Fractional integration; Mixture of distributions hypothesis; Return volatility; Spectral analysis; Trading volume. An extensive empirical literature has developed over the past decade for modeling the temporal dependencies in financial-market volatility. A common finding to emerge from most of these studies concerns the extremely high degree of own serial dependencies in the time series of absolute or squared returns and/or the estimated volatility processes. Bollerslev, Chou, and Kroner (1992) discussed over 200 of the earliest studies in this literature using autoregressive conditional heteroscedasticity (ARCH)-type models, and Ghysels, Harvey, and Renault (1996) provided a more recent survey of the literature on stochastic volatility models. Very little theoretical work has explored the structural determinants behind these dynamic dependencies. Meanwhile, numerous empirical studies have documented the existence of a strong positive contemporaneous correlation between trading volume and volatility [see Karpoff (1987) for an early discussion of this literature]. This positive correlation is consistent with most theoretical market microstructure models involving the strategic interaction among asymmetrically information-rational agents [see O'Hara (1995) for a survey of the relevant literature]. Unfortunately, these same theoretical models generally remain very vague, if not silent, about the long-run dynamic relationship between trading volume and volatility. A less structural approach for rationalizing the strong contemporaneous correlation between trading volume and volatility is provided by the so-called mixture-of-distributions hypothesis (MDH) pioneered by Clark (1973), Epps and Epps (1976), and Tauchen and Pitts (1983). According to the MDH, returns and trading volume are driven by the same underlying latent "news"-arrival, or information-flow, variable so that the arrival of unexpected "good news" results in a price increase, whereas "bad news" results in a price decrease. Both of these events are accompanied by above-average trading activity in the market as it adjusts to a new equilibrium. Accordingly, the absolute returns, or volatility, and trading volume should be positively correlated. Although the first generation of tests of the MDH by Harris (1986, 1987) and others were generally supportive of the model, subsequent studies by Lamoureux and Lastrapes (1994) and Richardson and Smith (1994) indicated that the same latent information-arrival process is unable to describe the short-run dynamic dependencies in both equity trading volume and volatility. More recently, however, Andersen (1996) argued that these apparent rejections of the MDH may be due to artificial and unwarranted distributional assumptions. Building on the Glosten and Milgrom (1985) market microstructure setting in which a riskneutral market maker posts competitive bid and ask prices, the resulting modified MDH with Poisson-distributed trading volume is not rejected for the same individual common shares that firmly reject the more traditional version of the MDH, assuming trading volume to be normally distributed. Meanwhile, the estimated joint latent information arrival processes indicate a surprisingly low degree of volatility persistence compared to the empirical results reported in the extant ARCH and stochastic volatility literature. In fact, this latter body of literature has led several studies (see, among others, Dacorogna, Miiller, Nagler, Olsen, and Pictet 1993;
doi:10.2307/1392235 fatcat:ka26cxlaonfirjefqfejsy62hu