The ACWI world composite, unadjusted for inflation, peaked in July 2024. The index is in the lineage of the US hegemonic 1807 36/90/90/54 year great x/2.5x/2.5x/1.5x four phase Fractal Series ending in 2074 with progenitor nadir valuations in 1842-43, 1932 and with an inflation adjusted peak in 2021.

From 1932 US equities followed a 10-11/21-22/21-22 year fractal series :: x/2x//2x ending in 1982 with high Volcker QT fed fund rates that have since cascaded lower and lower and post the 2009 global housing bubble have collapsed to near zero.

Low inflation during this low interest rate period was facilitated by imported low cost manufactured goods from China, use of natural gas as an energy source, and fracking which elevated US oil production and export to levels not seen in decades. During Covid large % GDP deficit spending, 2.5-3% mortgage rates, supply line disruptions, and corrupt corporate price fixing produced a 10% inflation rate. In response the US central bank invoked Volcker-like QT with an inversion of short term -long term bond yields that has lasted more than 600 days, longer than the inversion leading up to the 1929 crash.

The observed fractal series since 1982 is 13/31 of 32 years with an expected large scale 2024-2025 second fractal crash. (See main page of the Economic Fractalist). This is part of a 13/32/32-33/20 year :: x/2.5x/2.5x/1.5 x series ending in 2074. The third 32-33 year fractal starting in 2025 will see the greatest monetization of national debt and social contract liabilities in world histor.

The yearly fractal series groupings since 1982 can be observed using the SPX. The first 13 year fractal is composed of a 3/7/5 year series ending in 1994. The second fractal is composed of two series: 3/7/7 years and 4/8/7 of 8 years ending in 2025.

The terminal portion of the 1994 current 31 year second began in March 2020 and follows a 8-9/24/23 month :: x/2.5x/2.5x fractal growth sequence peaking(unadjusted for inflation) in July 2024. The 23 month third fractal of the 8-9/24/23 month series is composed of a 5/10/10 month series. The third 10 month series started in October 2023 and is composed of a 13/28 0f 32 week :: 59-60/149-150 day series expected to end on about 16 August 2024. This is the incipient 13/31 of 32 year 1982 31-32 year second fractal crash.

A Comparison of the underperforming French CAC,(now below its recent 6 month average)with the better performing world composite ACWI which contain US, Japanese, and Indian stocks is useful in defining the final daily fractal decay series which appears for the ACWI to have started on 28 June 2024 and is composed of a 7/13 of 16/14 day :: y/2-2.5y/2y series ending on 16 August 2024. Like the 11/26/28 day :: y/2.5y/2.5y decay series occurring in 1929, a significant rebound of global equities is expected to occur beyond the early November 2024 US presidential elections.

Fractal self-assembly and self ordering of asset valuations, traded daily (or five times a week), occur in combinations of three and four phase mathematical fractal series: x/2-2.5x/2-2.5x/1.5-1.6x and x/2-2.5x/1.5x-2.5x, where x denote a fractal time unit in days, weeks, months, and years.

An alternative 149-150 day DAX 17 January 2024 second fractal decay model of the 23 October 2023 60/125 day of 126 to 150 day first and second fractal series has no flash crash, rather a 14 July 2024 6/12/9-10 day :: x/2x/1.5-1.6x decay series ending 15-16 August 2024.

The current model for the DAX and western equity composites from the March 2020 covid low is an averaged 8-9/23-24/23/1 of 12-15 month :: x/2.5x/2.5x/1.4-1.6x four phase growth and decay fractal series.

The expected June- Sept 2025 low for global equities represents the end of a major consumer-citizen 1982 13/32-33 year debt-dependent credit cycle, where asset prices in the terminal 32nd/33rd year of he second fractal particularly, global residential asset and equity prices will fall precipitously and debt default and restructuring will occur, forming the basis for another 30-33 year inflationary credit expansion.

The expected incipient August September 2024 Fed fund rate cuts and mid August 2024 149-150 day second fractal nadir valuation saturation selling would provide two explanations for rebound valuation growth beyond the incidental US November 2024 election cycle.

The 1982 -2024 German DAX 13-14/30-31 year First and Second Fractals

Within the 4-phase 267 year 1807 to 2074 US hegemonic x/2.5x/2.5x/1.5x :: 36/90/90/54 year fractal series, rests an interpolated 1982 German DAX 13-14/30-31 year series. The 30 year second fractal nonlinearity could as an incipient feature have an initial shocking flash crash (with a sharp rebound beyond the November 2024 election.

The self-assembly fractal mathematical architecture of the 23 October 2023 to 5 July 2024 x/2x :: 13(-)/25-26 week :: 60/120 day fractal series is observable. Rather than 28 October 2023, the Incipient day for the 13-/25-26 week first and second fractal series is 23 October 2023 consistent with the fractal maxim that fractal valuation growth begins in terminal fractal decay. Objectively, a 13(-)/25 week first and second fractal series can be identified from 23 October 2023 to 5 July 2024. The first 13 week fractal occurs as a 3/7/5 week fractal series(x/2-2.5x/1.6x) and the second fractal, a 5/10/12 of 12-13 week fractal series x/2x/2.4x-2.5x. Next trading week, the 23 Oct 2023 x/2x series with a base (x) of slightly less than 13 weeks will be in the window (2x to 2.5x)of 26-32 week second fractal nonlinearity.

As of 5 July 2024, a 23 October 2023 60/120 day :: x/2x first and second fractal series is observable. The terminal fractal window begins next week  between day 121 and day 150.

The Dax is at/near its March 2020 third fractal apogee with a three phase fractal growth series of 8/24/23 months as of 5 July 2023. (see below.)

The extended second fractal of 24 months or 4/9/8/6 months :: x/2-2.5x/2x/1.5x is beyond the expected 2.5x or 20 months of the 8 March 2020 base fractal because of the extraordinary QE in 2020-2021 with the Fed adding 10-11 trillion dollars to their balance sheet or a historical 30 % increase in the GDP/national debt ratio in just two years. The last 5/10/10 month third fractal takes the DAX to its July 2024 lower high with a potential high next week completing a 4/10/6-10 day:: x/2.5x/1.5-2.5x 3-phase growth fractal series.(see the final green/yellow/orange 4/10/4 of 4-10 day growth series above).