Testing Fibonacci retracement bins with moving-average swings

Three inherited pullback marks

Technician lore in the source period treated a 33.3 percent pullback as the shallowest correction expected after late buyers exit an advance. The same lore treated a 66.6 percent pullback as the deepest correction still taken to mean that demand remained clearly stronger than supply.

Between those bounds, a 50 percent pullback was taught as the most common place for a correction to end, even though an exact 50.0 percent print was described as rare. Those one-third, one-half, and two-thirds marks were the candidate continuation levels later scored against measured corrections.

Swings locked by a moving-average cross

Reactionary lows and highs were labeled only after a close crossed a 13-day moving average, using the extreme close on the opposite side of that average. A reactionary high is the highest close while price remains above the moving average, recorded only after a later close falls below that average. A reactionary low is the lowest close while price remains below the moving average, recorded only after a later close rises above that average.

An uptrend required a pair of higher highs and higher lows, and a downtrend required a pair of lower highs and lower lows. Each correction was then sized as a percentage retracement of the immediately prior impulse in the same trend.

A sliding-bin count of the sample

On a continuous Treasury-bond series covering 15 calendar years, 150 corrections were recorded and every one measured between 9 percent and 100 percent of the prior move. Retracements beyond 100 percent were excluded as trend breaks.

Corrections were tallied in successive 10-percentage-point windows stepped by 1 percent from the 1 to 10 percent window through the 91 to 100 percent window. That sliding-bin count is a tally of corrections inside those advancing windows, from the shortest pullbacks to a full retrace.

Where the counts peaked

The resulting counts peaked in the 19 to 28, 43 to 52, and 77 to 86 percent windows, and 27 of the 150 corrections fell in the 43 to 52 percent window. The populated short and long peaks did not sit on the 33.3 percent or 66.6 percent marks, so those conventional minimum and maximum levels were not supported by the sample.

The half-retracement mark did fall inside the most populated window.