Constructing a weekly block-tick breadth z-score

The weekly three-way tape

Market-breadth in this construction is a tape-wide lean inferred from how large prints split among upticks, downticks, and unchanged sales rather than from one price path. The historical workflow therefore starts with three weekly series, not with a single plotted line.

Daily large-print counts are totaled into weekly uptick, downtick, and unchanged series covering all trades larger than 50,000 shares. An uptick is a sale priced above the immediately preceding trade, a downtick is a sale priced below that trade, and an unchanged print is a sale priced equal to it.

Exponential smoothing of each series

Each of the three weekly totals is smoothed with a 14 percent exponential average, presented as roughly comparable to a 13-week simple average. Exponential smoothing is a recursive average that blends a stated fraction of the newest weekly total with the complementary fraction of the prior average.

The exponential update is 14 percent of the newest observation plus 86 percent of the preceding average. The same update is applied separately to the uptick, downtick, and unchanged series so the later ratio compares three similarly smoothed counts.

A commitment-weighted tick-ratio

A single tick-ratio is then formed by subtracting the smoothed downtick series from the smoothed uptick series and dividing by the smoothed unchanged series. That is smoothed upticks minus smoothed downticks, divided by smoothed unchanged prints.

Unchanged prints sit in the denominator so the ratio rises when that middle count is small, on the premise that fewer unchanged trades mark stronger one-sided commitment.

A local mean, then a z-score

A 52-week moving average of the tick-ratio is calculated so the current ratio can be stated as a deviation from that local mean. The moving average is a fixed-lookback average of the tick-ratio used as the local mean against which the current reading is compared.

For charting, those deviations are converted to z-scores by dividing by the standard deviation of the preceding 52 weeks. The z-score is the current deviation from a 52-week mean of the tick-ratio, divided by the standard deviation of that same 52-week window.

Guides on the finished axis

Approximate scale guides are given as about half the readings between +0.67 and -0.67, about two-thirds between +1.00 and -1.00, and about 95 percent between +2.0 and -2.0. Horizontal chart lines at +1.0 and -1.0 standard deviations are described as isolating about one-sixth of observations in each tail.

Editorial reading: TradersWeek takes those guides as the last construction step, a shared axis for comparing weeks. The historical workflow does not turn the lines into a trading rule.