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I am writing a thesis on the concentration of frequent traders among all traders active in a particular stock during a day. I want to analyze the impact of the concentration on daily stock price volatility, liquidity (e.g., measured with turnover) and returns.

By concentration I basically mean the share one trader contributes to the total number of trades (or dollar trading volume) in a particular day.

My dataset is for one single stock only and quite rich: It provides intraday trading history of each trader buying or selling that stock as well as traded volumes, trade prices, etc. So far, I used a concentration ratio to compute daily concentration of traders in the stock. I computed the sum of trades of the largest five traders divided by the total number of trades on a particular day. (I also computed this for dollar volume.)

Well, now I want to run regressions like this one:

$ Return_t= \alpha + \beta \cdot ConcentrationRatio_t + \gamma \cdot X_t+ \epsilon_t$,

where $X_t$ might be controls.

My issues are currently the following:

The concentration ratio is usually higher on days with generally sparse trading. Then, a single trader can very easily impact the concentration ratio. As I expected, the correlation between concentration ratio and total number of trades per day is negative (in my sample it is about -0.4). On days with infrequent trading activity, I would, for instance, expect lower returns and lower liquidity. So, my concern is that the effects I am willing to estimate with my regression specified above come from a different channel.

Therefore, I am not sure whether this is the best approach to encounter this research task. Since my experience with regression analyses is not really high, I am unsure whether there might be some econometric concerns hidden in my plan. Also, maybe someone has a more appropriate measure to proxy for concentration among trading activity? I would appreciate to hear your opinion.

Thank you. :)

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1 Answer 1

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You should be able to account for this in the volatility and return regressions by including the daily trading volume or turnover as an explanatory variable. A correlation of 0.4 should not cause collinearity problems.

Obviously this will not work for turnover as a dependent variable. Personally I would just avoid using turnover as a liquidity measure, as there are better measures of liquidity available anyway. If you have quote data for this stock then you could compute the average quoted bid-ask spread and the average effective spread. If you only have trade prices you could use the Roll Measure.

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