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Trade-time clustering


We introduce an intraday measure of trade-time clustering which estimates periodic grouping of trades, integrating volume and trade duration. This measure consistently detects informed trading superior to volume and duration. We find that in stable markets, both lagged information flow and liquidity are positively associated with trade-time clustering, while in volatile markets only lagged liquidity is. Trade-time clustering is positively associated with contemporaneous price impact, price volatility, and market efficiency, suggesting that trade clustering contributes to price discovery. Following increased trade-time clustering, we observe more aggressive orders from informed traders, but less high-frequency trading in stable markets.

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  1. While we use 5 min intervals to examine the intraday determinants and effects of time clustering, the same calculations can be applied to different time intervals for different purposes e.g. daily time clustering, 1 min, 1 s, etc.

  2. We do not assert that time precedence suggests causation. Rather, we are exploring associations between time clustering and pre-existing market conditions.

  3. See Bessembinder and Kaufman (1997), for the discussion on the difference between quoted spread and effective spread.

  4. Bertsimas and Lo (1998) theoretically explore the relation between order splitting strategy and trading cost.

  5. Chakravarty, Jain, Upson, and Wood (2012) show that ISO orders are associated with informed institutional trading.

  6. Located at

  7. As a robustness test, we also define duration as the average time between trades t and t-1 and trades t and t + 1. The results are qualitatively similar.

  8. In the rare case that we encounter multiple (j) trades at the same timestamp, the duration of all but the first listed trade is calculated as 1/j milliseconds.

  9. In the online internet appendix (, we demonstrate several scenarios of possible trading patterns and show how trade-level and aggregate time clustering correctly identifies concentrated trading, while not being biased by overall volume and average duration.

  10. Chiyachantana et al. (2004) find that the price impact of institutional (block) trades varies under different market conditions. The price impact is higher for of institutional buy orders in bullish market while it is higher for institutional sell orders in bearish market. They argue that these institutional trades are on the same side of the market and liquidity demanders, and thus have higher trading cost. Trade-time clustering might have the same pattern as price impact of institutional trades because time clustering is likely driven in part by with institutional trading.

  11. The list of the stocks in our sample can be provided as requested.

  12. See Appendix Table 10 for variable calculation descriptions.

  13. We measure informed trading using price impact, rather than PIN or PPIN, as in Aslan et al. (2011), because Duarte and Young (2009), Mohanram and Rajgopal (2009), and Lai et al. (2014) show that PIN can be largely correlated with illiquidity as distinct from adverse selection.

  14. See Kim and Stoll (2014) for additional proxies of informed trading.

  15. The Seemingly Unrelated Regressions (SUR) process estimates the simultaneous variance–covariance of the coefficients of different models, and thus allows to examine the equality of coefficients across models using Chi-squared test.

  16. However, it should also be noted that during the stable subsample, the S&P 500 increased by 0.17% while the S&P 500 decreased by 4.53% during the volatile subsample. The large market downtrend in the volatile subsample could be influencing these results more than volatility alone.

  17. Due to their redundancy, these results and pertinent discussion are available in the internet appendix (

  18. We confirm that these results also hold when regressing time clustering on the hypothesized variables of interest (and controls), both individually and in the same regression model. The results are omitted from the paper due to their similarity but are available upon request.


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Correspondence to Wei Sun.

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For helpful comments and suggestions, we thank Tom McInish, James Upson, Robert Van Ness, and the seminar participants at the Financial Infrastructure Stability and Cybersecurity Center, University of Memphis, University of Mississippi, University of Texas at El Paso, Saginaw Valley State University, Eastern Finance Association, Southern Finance Association, and Financial Management Association. The opinions expressed are those of the authors and do not necessarily reflect those of the Office of Financial Research in the US Department of the Treasury, where Professor Jain is a fellow.

Appendix 1

Appendix 1

See Table 10.

Table 10 Variable description

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Black, J.R., Jain, P.K. & Sun, W. Trade-time clustering. Rev Quant Finan Acc 60, 1209–1242 (2023).

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