نوسانات و معاملات تحقق یافته

This paper re-examines the impact of number of trades, trade size and order imbalance on daily stock returns volatility. In contrast to prior studies, we estimate daily volatility using realized volatility obtained by summing up intraday squared returns. Consistent with the theory of quadratic variation, realized volatility estimates are shown to be less noisy than standard volatility measures such as absolute returns used in previous studies. In general, our results confirm [Jones, C.M., Kaul, G., Lipson, M.L., 1994. Transactions, volume, and volatility. Review of Financial Studies 7, 631–651] that number of trades is the dominant factor behind the volume–volatility relation. Neither trade size nor order imbalance adds significantly more explanatory power to realized volatility beyond number of trades. This finding is robust to different time periods, firm sizes and regression specifications. The implications of our results for microstructure theory are discussed.

There is a large empirical literature on the relationship between trading volume and volatility. This research is important in providing insights into how market participants process and react to new information. Efforts in this direction can be seen from recent research focusing on the impact of different components of trading volume on volatility. For example, Jones et al. (1994) decomposes daily trading volume into number of trades and average trade size and examines their impact on the volatility of NASDAQ stocks. They find that number of trades explains virtually all of daily volatility, with trade size playing a minor role. This result is startling as it runs counter to standard market microstructure theories which emphasize the role of trade size as a signal of informed trading. Traditional microstructure theories e.g., Kyle, 1985 and Admati and Pfleiderer, 1988 also focus on order imbalance as a signal of informed trades. It is assumed in these models that market makers will adjust prices upwards (downwards) when there are excess buy (sell) orders. Thus, price volatility may be induced by net order flow. Consistent with this prediction, Chan and Fong (2000) find that a substantial portion of daily stock returns is explained by order imbalance. Although they do not test the direct impact of order imbalance on volatility, they find that after filtering the effects of order imbalance on returns, number of trades explain very little of the absolute residuals. They conclude that it is order imbalance, rather than number of trades that drives the volume–volatility relation. We argue that this conclusion may be premature. First, prior studies, including Jones et al. and Chan and Fong use absolute returns as the measure of daily stock returns volatility. It is well known, however, that absolute returns are a very noisy estimator of the true latent volatility. Since daily absolute returns are computed using only two prices (opening and closing), the computed volatility may be very low if the opening and closing price happens to be very close, even though there might be significant intraday price fluctuations. The fact that absolute returns are measured with substantial noise prompts the following question: would the results of prior studies hold if one uses a more precise estimator of the unobserved volatility? This paper answers this question by using realized volatility in place of absolute returns as the volatility measure. Following Andersen et al., 2001 and Andersen et al., 2003, we compute daily realized volatility using intraday returns sampled at 5-min intervals. Andersen et al. (2001) shows that in the limit, sampling at sufficiently high frequency leads to a daily volatility estimate that is indistinguishable from the true latent volatility. Consistent with this prediction, we find that our realized volatility measure is substantially less noisy than the corresponding absolute returns measure. Using realized volatility as the volatility measure, we show that number of trades explains far more of daily stock return fluctuations than has been documented in prior studies. Specifically, over our sample period (1993–2000), number of trades explains about 42% of daily realized volatility for the 30 stocks comprising the Dow Jones Industrial Average index. In contrast, average trade size and absolute order imbalance accounts for only 25% and 27% of realized volatility respectively. Adding average trade size and absolute order imbalance adds very little explanatory power for realized volatility beyond number of trades. These results are robust to sub-periods, firm sizes and higher-frequency realized volatility estimates as suggested by some recent studies (Bandi and Russell, 2003). Our results confirm the findings of Jones et al. (1994) that number of trades is indeed the dominant factor in the volume–volatility relation. The rest of this paper is organized as follows. Section 2 reviews the theoretical literature. Section 3 describes our data and methodology. Section 4 presents summary statistics of the data. In Section 5, we examine the impact of trading volume and its two components, number of trades and average trade size, on absolute returns and realized volatility. Section 6 tests the robustness of our results to trends in trading volume. The role of order imbalance in explaining realized volatility is examined in Section 7. Section 8 concludes with a discussion of main implications of our findings and some directions for future research.

Recent research on the volume–volatility relation has focused on the role of number of trades, trade size and order imbalance. Using realized volatility computed from 5-min intra-daily returns, we examine the joint impact of all three trade measures on the volatility of daily stock returns. Consistent with the theory of quadratic variation, we find that absolute returns contain a substantial amount of measurement errors and hence, do not provide a basis for reliable inferences in volume–volatility studies. Results based on realized volatility show that number of trades explains far more of daily volatility than has been documented in prior studies that use absolute returns as the volatility measure. On average, number of trades explains about 42% of daily realized volatility for stocks in the Dow Jones Industrial Average stock index. This finding is robust across time, firm size and use of higher frequency data for realized volatility. While the volatility impact of trade size and order imbalance are both statistically significant, they add little explanatory power to realized volatility beyond the number of trades. Overall, our results confirm those of Jones et al. (1994) that number of trades explains a substantial component of daily realized volatility, with trade size playing a minor role. This is consistent with the mixture of distributions hypothesis which emphasizes the role of trade frequency as measure of information arrivals. The significance of number of trades is also consistent with the presence of stealth trading. That is, informed investors may break up larger trades into many small ones to hide their private signals. This implies that number of trades ought to have more information content for stock price volatility than trade size. Our analysis show that it does. Our results for order imbalance are intriguing given that standard microstructure models such as Kyle, 1985 and Admati and Pfleiderer, 1988 also emphasizes the role of net order flow in inducing price changes. A plausible reason why order imbalance does not capture a substantial portion realized volatility for the Dow 30 sample is that these firms are likely to be efficiently priced most of the time, and hence they attract mostly noise traders. Empirical evidence appears to confirm this. Using data for 90 NYSE stocks, Easley et al. (1996) finds that “the probability of information-based trading is lower for high volume stocks” (p. 1405). Similarly, Andersen et al. (2001) finds that for large capitalization stocks, noise trading accounts for about 60% of the daily de-trended volume.10 Furthermore, Easley et al. (1997) show that the trading behavior of uninformed investors is positively autocorrelated, and that this causes sequences of orders to be less informative to market makers than is predicted by standard microstructure theories. This may explain the relatively weak explanatory power of order imbalance for realized volatility.