Inferring Trade Direction Revisited

I had to read this paper again after ~1.5 years as I had forgotten the basic idea behind the classification. My understanding, this time was far better than the previous encounter. In this post, I will list down a few points form the paper

One can think of three ways to classify trades as “buy” or “sell” trades.

Tick test : Compare the current trade price to the previous trade price
uptick : current trade price is higher than the previous trade price
downtick : current trade price is lower than the previous trade price
zero uptick : current trade price is same as previous trade price that is preceded by a uptick
zero downtick : current trade price is same as previous trade price that is preceded by a downtick
uptick+zero upticks are classified as “buys” and downtick + zero downticks are classified as “sells”
Reverse Tick test : Compare the current trade price to the next trade price
uptick next : next trade price is higher than the current trade price
downtick next: next trade price is lower than the current trade price
zero uptick next: next trade price is same as current trade price that is preceded by a uptick
zero downtick next: next trade price is same as current trade price that is preceded by a downtick
uptick next +zero uptick next are classified as “sell” and downtick next+ zero downtick next are classified as “sells”
Based on Quotes : Look at the prevailing quote for the trade
If the trade is at ask or higher, then the trade is “buy”
If the trade is at bid or lower, then the trade is “sell”
If the trade is within the bid-ask, then whichever side the trade is closer to, classify the trade accordingly
Uncertainty about the direction that are exactly at the midway between bid ask

What are the findings ?

When the trade is bracketed by a price change, both tick test and reverse tick test gives the same classification. If the trade is bracketed by a price continuation, the classification differs. In the case of trade continuation, the availability of quote data helps. If a quote increase is in the direction of the preceding trade, then tick rule performs better. Based on the prevailing quote, the authors, they find tick test to perform better than reverse tick test
Large percentage of quote revisions happen before trade happens and hence choosing the current quote for classification could lead to faulty classification
If the new quotes are recorded ahead of the trade, then using the current quote should cause a larger number of trades to appear within the bid ask
In the dataset used by the authors, they find that there is a sharp fall off of quote revisions 5 seconds before the trade and hence they hypothesize the following : If the current quote is less than 5 seconds old, use a time delayed quote
What is the result of using current quote rather than 5 second prior quote ? There will be many trades that fall within the spread.
The analysis shows that the classification based on the previous quote is better than the current quote in all cases of unidentified quotes
Using a simple Poisson model, the authors show that tick test performs better for the trades at the mid point of bid ask of the prevailing quote.

Based on these findings, the authors propose a trade classification algorithm:

Lee and Ready algorithm :

If the current quote is less than 5 seconds old, use time delayed quote as “prevailing quote”, else use the current quote as ‘'”prevailing quote”
Trades at the ask or above it are classified as “buy”
Trades at the bid or below it are classified as “sell”
Trades inside the spread and close to ask are classified as “buy”
Trades inside the spread and close to bid are classified as “sell”
Trades at the midpoint of prevailing quote are classified based on tick test

Takeaway:

There are two takeaways from this paper. One is that “tick test” is highly accurate. Second is that the classification based on current quote needs to be looked in to carefully. One might have to consider a delayed quote as the “prevailing quote” in order to classify a trade correctly.