Constructing advance-decline breadth indicators

Three daily closing-price states

Every advance-decline construction is assembled from three daily closing-price states: an issue can advance, decline, or remain unchanged. Those three outcomes are the advance-decline components of the series.

Standalone advance and decline counts are treated as weakly informative. Constructions therefore compare those counts rather than reading either total on its own.

Difference constructions and ratio constructions

With the daily counts held fixed, constructions fall into two families: difference formulas and ratio formulas. Each family ranges from one-step to multi-step designs.

A difference construction starts from the signed or unsigned gap between advancing and declining issues. A ratio construction scales a count or a difference by declines, by advances plus declines, by unchanged issues, or by all issues traded.

What belongs in the denominator

Ratio constructions change meaning when the denominator changes from declines only, to advances plus declines, to all issues including unchanged.

One variant places a 30-day average of advances over a 30-day average of declines rather than averaging the daily ratio itself.

Hybrid constructions divide the signed or absolute advance-decline gap by unchanged issues or by total issues traded. Another form accumulates a square-root transform of advance-to-unchanged versus decline-to-unchanged ratios. Another sums a weekly difference-over-unchanged series and compares it with a price index by regression.

Smoothing and running sums

Nearly every construction is then smoothed. Breadth smoothing is a simple or recency-weighted moving average, or a running sum, applied so noisy daily counts can be read as internal trend. The smoother is defined by lookback length and by whether recent observations receive extra weight. Shorter recency-weighted averages are described as the most sensitive to turns lasting days or at most weeks.

A running sum of daily advances minus declines is offered as an alternative to moving-average smoothing. Because the plotted level depends on the start date, only slope, momentum, and comparison with the prevailing price trend are treated as meaningful.

One difference-family oscillator is defined as the 19-day exponential average of advances minus declines minus the 39-day exponential average of the same series, using 10 percent and 5 percent smoothing factors. A companion series is formed by accumulating the daily oscillator values.

Participation and formula-specific scale

A falling breadth trend against a rising price index is framed as fewer issues supporting the advance. A rising breadth trend against a falling index is framed as fewer issues supporting the decline. Both are treated as change-of-trend hypotheses that often fail.

Extreme-zone readings, when used, are not universal. Each formula-and-smoother pair produces its own scale. Values near zero are typically treated as indeterminate.

Procedural selection, not a preferred formula

Selection guidance is procedural rather than a single preferred formula. Use counts that are obtainable, study at least six months of the chosen series, begin with longer trendlines rather than extreme levels, and treat breadth as a supplement to an independent reading of price-trend direction and maturity.