The 40-week cycle, also known as the 9-Month Cycle, is a cornerstone of J.M. Hurst’s Cyclic Theory, developed during the 1960s and 1970s to forecast financial market movements through harmonic cycles. Spanning approximately 272.8 days from trough to trough, it consists of two 20-week cycles (19.48 weeks or 136.4 days each). The 40-week cycle is additionally subdivided into four 10-week or 80-day cycles (68.2 days), eight 40-day cycles (34.1 days), sixteen 20-day cycles (17 days), thirty-two 10-day cycles (8.5 days), and sixty-four 5-day cycles (4.3 days), forming one nested structure essential for swing and position trading.
This idealized 40-Week Cycle (purple) of 272.8 calendar days is divided into two 20-week cycles (teal), each
of which is further divided into two 10-week cycles (blue), highlighting the complete nested harmonic structure.
Note that the 40-week cycle is itself half of the 18-month cycle, which in turn is one-third of the 54-month cycle—half of a 9-year cycle—and so on. The 40-week cycle’s intermediate-term horizon captures significant market swings, making it ideal for timing entries at troughs and exits at peaks, especially when aligned with shorter cycles (10-week, 20-week) or longer cycles (18-month, 54-month).
The nominal 40-Week Cycle as a part of greater Hurst cycles.
Current S&P 500 Hurst Cycles: Long-term, 18-year cycle upward, peaking 2028-2030, trough by 2036; 9-year cycle bullish, peaking 2026-2027, trough 2028-2030; 54-month sub-cycle upward, trough December 2026. Medium-term, 40-week cycle bullish; 20-week cycle downward, trough late August/early September 2025. Short-term, 80-day, 40-day, 20-day cycles downward, synchronous, with troughs August 18-20 (20-day), August 22-26 (40-day), end September (80-day). Considering over 300 years of US stock market data, major troughs occurred in 2008 (72-year), December 2019 (9-year), with 18-year trough expected ~2029. Longer-term 36-, 72-, 144-year cycles exert gradual influence; 144-year cycle, bottomed 1932, now declining, though markets may rise before full impact.
54-month, 18-month, and 40-week cycles in the CAD/USD (weekly bars), 2020-2025.
Bitcoin (monthly bars): 18-month and 54-month cycle peaks and troughs, 2018-2027.
In bear markets, the cycle’s crest occurs early (second to third month, left translation), with a brief rise and prolonged decline; in bull markets, the crest shifts later (sixth to eighth month, right translation), leading to a longer advance. The strongest rallies typically occur in the first three months when cycles align upward, while the last three months are vulnerable to renewed declines.
Why the turning points of individual long-term cycles typically diverge—often significantly—from the composite
or summation cycle of the three to four most prominent cycles (red), and thus from actual market price extremes.
Hurst's nominal model allows for significant variability in actual cycle lengths
Hurst's Nominal Model can be displayed as a series of sinusoids (x-axis) with different amplitudes (y-axis) that, when summed, create a composite model, represented by the thick black line in the following charts. J.M. Hurst's concept, termed "sigma-l," represents the sum of all cycles within a system, assuming an infinite series of cycles with increasing periods. This underlying trend, conceptualized as the sum of sinusoidal functions, is dynamic and never static. It may appear flat during sideways consolidations of shorter cycles, but this reflects the influence of a much larger cycle, relative to the cycle in focus, turning upward or downward.
40-Week Cycle without or neutral trend.
The above flat or neutral model of a 40-week cycle assumes a non-existent sigma-l, meaning its value is zero. In real markets, this is never true but may be approximated when a much longer cycle is turning upward or downward.
40-Week Cycle with bullish trend.
The above bullish model of a 40-week cycle features a positive underlying trend that modulates the composite summation, causing already bullish FLD interactions to significantly exceed upside targets. Interactions previously expected to meet downside targets will now be undershot.
40-Week Cycle with bearish trend.
The above negative model of a 40-week cycle features a bearish (negative) underlying trend that modulates the composite summation, causing already bearish FLD interactions to significantly exceed downside targets. Interactions previously expected to meet upside targets will now be undershot.
The addition of an underlying trend impacts the summary status
of each interaction in the series, influencing decisions.
The tabulation above summarizes each 20-day FLD interaction within the idealized 40-week period, based on the previously described neutral, bullish and bearish models. M-Sigma indicates the trade direction and strength of interactions when the underlying trend is assumed to be zero, representing a localized subset of the underlying trend.
Subsequent summary columns reflect the differences when the underlying trend is bullish or bearish, providing a truer representation of Sigma-L. This better aligns with real price action in financial markets.
When accounting for the underlying trend, the summary columns show that in a bullish scenario, trends previously labeled as "risk buy" become standard "buys," some "buys" escalate to "strong buys," and so forth. The underlying trend amplifies bullish signals and weakens bearish signals. Conversely, a bearish underlying trend has the opposite effect.
Example of an 18-month cycle projection for the current S&P 500 in the chart below:
18-Month Cycle Projection for the S&P 500 based on Hurst's Nominal Model: A 9-year cycle trough hit in December 2019, followed by the March 2020 pandemic 18-month cycle trough. The 54-month cycle trough of October 2022 is rising, set to peak in early 2026. The 9-year cycle, likely peaked in 2023, is declining, but slow movement maintains bullishness, possibly linked to an 18-year cycle trough. An 18-month cycle trough formed in early April 2025.
The orange line is the 18-month cycle (17.93 months = 546.6 calendar days), the light green the 40-week cycle (9 months = 38.97 weeks = 272.8 days), dark green the 20-week component (4.5 months = 19.97 weeks = 136.4 days), light blue the 10-week cycle (= 68.2 days), dark blue the so called 40-day or 5-week cycle (= 34.1 days) and finally the so called 20-day cycle (17 days) is the purple sinusoid. The X axis represents the number of calendar days.
In the S&P 500, April 7, 2025, was an 18-month cycle low, and the next 40-week cycle troughs are estimated for early 2026 and late Q4 2026.
The
wavelengths in the above S&p 500 projection are average values rather than exact measurement. The
thick black composite line ignores the effects of both the trend and
cycles shorter than 20 days or longer than 18 months. Assuming the US
stock market operates with clockwork precision (which it does not, see Hurst's Principle of Variation), the dates for upcoming peaks and
troughs were
calculated from the 18-month cycle trough on April 7, 2025, and the
aforementioned average cycle lengths.
is projected to peak on August 19, 2025, according to Sigma-I.net.
See also:
Comparison of Hurst’s Cyclic Theory and Spectrum Cycle Analysis.
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