Roll [1984] proposed a model for the bid-ask spread that was based on first-order serial correlation.  His empirical tests were based on daily and weekly frequency equity data, and based on the results he concluded there were informational inefficiencies (or that there was very short term non-stationarity in expected returns).

More recently this model has been applied to high frequency data by Hasbrouck in his comprehensive book “Empirical Market Microstructure” [Oxford University Press, 2007].  In it he proposes the Roll model as a means of distinguishing between “price components due to fundamental security value and those attributable to the market organization and trading process.”  In other words this could be a means of observing the flow of “private”  information into the market.

This blog posting analyzes recent natural gas futures prices to look for intraday fluctuations in the flow of private information using the Roll model.  It asks the question: are there particular times of the day when private information flows are greater?  Is there a way of observing real time, at short time scale, when private information is flowing into the market with a view to improving transactional activity.

To summarize the Roll model briefly it proposed that the bid-offer spread should be equal to 2 x sqrt(-cov).  Where cov is the serial covariance of price changes.

Data

The data source for this analysis is CME/NYMEX NG Oct-2010 futures contract market data.  The data is available on a per tick basis, however to calculate serial covariances and other time based measures, the data is sampled on a one second basis.  Other sampling approaches are possible.  This data is from 8/31/2010.

The NG futures market trades 23 ¼ hours per weekday electronically.  However the pit session is from 9am to 2:30pm and constitutes a time of significantly increased trading volume and liquidity.  Therefore it is interesting to observe this daily discontinuity in the electronic data as market volumes increase.  Do pit traded volumes add to the information in the marketplace?  Do pit traders have private information about the market?

Looking at the data from two minutes before the open to two minutes after the open we can observe this in action.  If we take this 4 minute window and calculate serial correlations with a 30 second lag then we have 3 ½ minutes of data or 210 data points for this example.  Looking at raw price changes in ticks we don’t see any obvious patterns.  The data is scattered around 0 as we would expect with some outliers representing big moves: 

If we move to the prices level itself, we see that prices increased significantly after the open:

Now, looking at the theoretical bid-offer spread:

We can see that immediately at the open, there was a significant flow of private information into the market although it was brief.  After 30 seconds, the serial covariance lookback window, we see that this has already dropped.  In other words, the private information that floor trading brought to the market on this day was short lived, even though prices continued to rise.

Since we have actual bid-offer spreads for this same time horizon we can calculate the ratio of the theoretical to the actual.  Actual bid-offer spreads are limited to a lower bound of 1 tick.  When we calculate the ratio we find that it is similar to the prior chart:

For part of the time that private information is coming to the market, the bid-offer spread gets wider to accommodate this as market participants take a wait to see approach to the market.

More generally it would be nice to know when this information flow is prevalent.  Hedgers or price takers in the market may be inclined to wait for private information to flow through the market.  At the same time proprietary strategies may attempt to get in front of this information flow.  In this example, taking the lead from the market and buying immediately based on the private information flow would have led to short term profits by the end of the 2 minute time window shown here.

Similar examples can be seen at other times of day and on other days.

So in conclusion, the flow of private information to the market can be measured; traders would do well to take heed of it.