Constructing nested four-year market cycles

Two scales of cycle construction

The construction sets a long-term market form so that rising and falling phases both overshoot a central value band rather than reversing at fair value. The shorter repeating advance-and-correction unit is the dominant-step. Successive dominant-steps are assembled into a nested-envelope.

Valuation-extreme markers

An approaching up-to-down phase change is marked when average price-to-earnings moves above 20 and average dividend yield falls near 3 percent.

A down-to-up phase change is marked when average dividend yield rises above 6 percent and average price-to-earnings settles near 6 or 7.

Shape of the dominant-step

The shorter rhythm used as the model building block measures about 4.3 years during the rising half of a 33-year envelope and about 3.9 years during the falling half.

That shorter rhythm is shaped as roughly three years of advance followed by about one year of decline that is treated as a stabilizing reset inside a positive-feedback market.

Participant-rotation at the peak

The construction assigns three participant roles, investors, traders, and novices, and locates the cycle peak at the point where all three groups are ready to switch from buying to selling. That sequenced entry and exit is participant-rotation.

Later four-year steps inside the rising envelope are described as carrying more novice participation and deeper required corrections until a correction matches or exceeds the prior advance and the envelope turns down.

Nesting steps in a longer envelope

One completed 33-year analog is bounded from 13 June 1949 to 12 August 1982. Nominal four-year step plots show the rising envelope clearly, while a real-price-comparison that uses an inflation-adjusted broad-index series is used to reveal the later declining envelope.

Duration-split in the real-price-comparison

In the real-price step model, rising and falling phases are separated mainly by duration. An up-phase advance lasts 3.55 years against a 0.79-year correction, while a down-phase advance shrinks to 2.37 years and the correction lengthens to 1.56 years. That duration-split attributes phase outcome to how long advances and corrections last rather than to a change in their slopes.

Holding-window check

A holding-period volatility plot is offered as mathematical support that most reduction in variability of a market average occurs inside the first four years, with only a small further gain when the window spans two such intervals. The holding-window is the multi-year span over which averaging a market series is said to enclose one complete shorter cycle.