Realized volatility and transactions

https://doi.org/10.1016/j.jbankfin.2005.05.021Get rights and content

Abstract

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.

Introduction

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, 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, 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.

Section snippets

Review of the literature

Extensive evidence indicates that trading volume and stock returns volatility are positively correlated (see e.g., Karpoff, 1987, Gallant et al., 1992). Although many theories attempt to explain this correlation, there is no consensus on what are key factors behind the volume–volatility relation. Two paradigms have dominated this debate. The first (and older) paradigm is the mixture of distributions model (MDM) in which information arrival is the latent factor that jointly drives price changes

Data sources

Our sample consists of the 30 stocks in the Dow Jones Industrial Average stock index (hereafter, the Dow 30) as of June 30, 2000. The sample period is from January 1, 1993 to June 30, 2000, a total of 1893 trading days. We choose the Dow 30 because these stocks are very actively traded and hence, yield sufficient high frequency intraday returns for computing reliable daily volatility estimates. Information arrival rates for these stocks are likely to be high as well (Easley et al., 1996), a

Descriptive statistics

Table 1 reports summary statistics of volatility and volume for the Dow 30 stocks. We group the 30 stocks into size quintiles based on their market capitalizations as of January 1, 1997, the midpoint of the sample period. Panel A reports volatility statistics using absolute return residuals and realized volatility.

Absolute return residuals are obtained by running the following time series regressions:Rit=k=15αˆikDkt+j=112ωˆijRit-j+εit,where Rit is the return of stock i on day t, Dkt’s are

Absolute residuals regressions

Jones et al. (1994) report the startling finding that number of trades provides virtually all the explanation for the daily volatility of NASDAQ stocks. To see if their results also hold for the Dow 30, we apply the two-stage regression methodology used by them to our sample. The first-stage regression is given by Eq. (1). For each year, we regress the daily returns for every stock on a Monday dummy, and 12 return lags to account for movements in conditional expected returns. In the second

Volume de-trending

Gallant et al., 1992, Andersen, 1996 point out that over long periods, trading volume shows a distinct upward trend, which needs to be removed before fitting to the data. Time series plots for the Dow 30 stocks show that the Dow 30 stocks also exhibit an upward trend.8 To test whether our previous results are induced by trends, we employ the moving average method used by Andersen (1996) to de-trend raw volume and number of trades for each stock.

Does order imbalance explain realized volatility?

A central prediction of microstructure theory is that trade takes place because investors possess different information or because of differences in beliefs. Since market makers are bound to trade with both informed and uninformed investors, they may use net order flow to infer the probability of informed trades and adjust quotes accordingly. Thus, order imbalance may be a source of price volatility. On the other hand, Easley et al. (1997) posit that standard microstructure theories may have

Conclusion

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

References (42)

  • R.D. Huang et al.

    Trading activity and stock price volatility: Evidence from the London Stock Exchange

    Journal of Empirical Finance

    (2003)
  • G. Kaul et al.

    Price reversals: Bid–ask errors or market overreaction?

    Journal of Financial Economics

    (1990)
  • O. Kim et al.

    Market reaction to anticipated announcements

    Journal of Financial Economics

    (1991)
  • C.M.C. Lee et al.

    Inferring investor behaviour: Evidence from TORQ data

    Journal of Financial Markets

    (2000)
  • R.C. Merton

    On estimating the expected return on the market

    Journal of Financial Economics

    (1980)
  • E.R. Odders-White

    On the occurrence and consequences of inaccurate trade classification

    Journal of Financial Markets

    (2000)
  • A.R. Admati et al.

    A theory of intraday patterns: Volume and price variability

    Review of Financial Studies

    (1988)
  • T.G. Andersen

    Return volatility and trading volume: An information flow interpretation of stochastic volatility

    Journal of Finance

    (1996)
  • T.G. Andersen et al.

    Modeling and forecasting realized volatility

    Econometrica

    (2003)
  • T. Ane et al.

    Order flow, transaction clock, and normality of asset returns

    Journal of Finance

    (2000)
  • Bandi, F.M., Russell, J.R., 2003. Microstructure noise, realized volatility and optimal sampling. Working Paper,...
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