**Market Data Questions**

# Decimalization and its Effect on Breadth Numbers

The standard price increment for stock trading for many years was 1/8 of a point. The reason for that increment goes back a couple of centuries to the way that stock prices were set as fractions of a ship's cargo value. It was a great system for the specialists who operated on the floor of the exchange, because the bid-asked spread was usually that 1/8 of a point, so the specialists could scalp that 1/8th point spread.

On June 24, 1997, the NYSE implemented a change by shrinking that increment to 1/16 of a point. The exchange made the full conversion to decimal trading, with prices having one penny increments, on January 29, 2001. This change was bad for the specialists, who lost that big spread, but better for individual traders and investors who benefited from the smaller spreads.

One of the biggest changes for technical analysts that resulted from this rule change has to do with the market breadth numbers. It used to be that the issues which closed unchanged each day averaged about 20% of the total number of stocks that traded each day. When measuring advances and declines for indicators like the A-D Line or the McClellan Oscillator, unchanged issues get no vote. Back when a stock had to change its price by at least 1/8 of a point, it took a lot more buying or selling pressure to move the share price off of the prior day's value.

But it does not take as much pressure to move a stock by just a penny, which is the new increment. So a stock that changes by a penny gets the same vote in the A-D statistics as one that changes by a dollar. Ever since decimalization went into effect, the number of unchanged issues each day has shrunk to around 5% or less. This means that there are a lot more voters now each day when the advancing and declining issues are tabulated, and some technicians have contended that these additional voters have ruined the A-D stats.

To test that hypothesis, I did a study back in 2004, using data available by subscription from the NYSE that contained the closing price and amount of change for each stock that traded each day. I used data covering the period from Nov. 1, 2001, to April 16, 2004 as a test period. This was after decimalization went into effect, and we cannot go back to the pre-decimalization days to try an model what it would have been like had decimalization been in place back then. We can only look at the post-decimalization era to see what the effect is.

Having assembled all of this data for each of the trading days in our test period, I then wrote spreadsheet formulas to examine each of the stocks who changed each day by 1/16th of a point or less (0.0625). For the purposes of the study, I made the assumption that if the old days of 1/8 point ticks were still with us, then if a stock changed by an amount greater than 1/16th of a point, then the rounding effect would each that 1/8 point tick level, and so that stock would be a legitimate voter. If a stock changed by 6 cents or less, I counted it in the "sub-tick" group. This is a somewhat faulty assumption, since in real life a lot of other things can happen in the trading environment which would have affected whether a stock was up or down on a given day. Also, a stock could have advanced by 2 cents per day for 5 days, and been counted as a "sub-tick" issue each of those days, even though the cumulative effect would have triggered the counting of a full tick change at some point along the way. I recognize that this is only a poor approximation of what real life might have been like had decimalization not been imposed, but given the data we have there is little else that we can do.

After filtering the stocks based on whether their change was big enough to have counted in the old days, I could then calculate daily A-D numbers for the stocks which had real changes by an amount greater than the old "tick" definition, and also A-D numbers for the "sub-tick" group. The chart below shows the results of that study for this limited time period. What I found was that the movements of the sub-tick group tend to match the movements of the big move group. Saying it more plainly, if the overall NYSE sees a 2 to 1 up day for advances versus declines, then the sub-tick group tended to also see a strong positive bias.

This chart shows cumulative A-D ratios, and so each group appears equal in chart magnitude. If I showed raw A-D Lines, then the sub-tick group's A-D Line would show much less magnitude of its movements because of the small total number of issues in that group. The reason I did it this way is to help see the correlation of the movements of the sub-tick A-D Line with the composite one. The point I wish to convey is that while the sub-tick stocks do change the A-D numbers somewhat, the effect is not as great as we might think because of the factor of these sub-tick numbers tracking the ratios seen in the overall market.

I should further emphasize that this was merely an investigative study, hoping to learn more about the effects of decimalization on this data, and this is not a complete trading system or even a complete analysis of the full implications of decimalization for all time. But it was enough of a finding from this limited period to lead me not to worry much about the effects of decimalization on the A-D numbers.