"The Mandelbrot Fractal Dimension" signals that the crash is getting closer. Is the "safe-haven investment moment" in the US stock market already here?

According to the Zhitong Finance APP, the well-known Wall Street investment institution BCA Research recently released a significant warning study. The institution stated that the "260-day complexity indicator" of the MSCI AC World Index, which measures the trends of global stock markets, triggered a "sell" signal in mid-October 2024, indicating that the vast majority of global stock markets will enter a consolidation and fluctuation period lasting until mid-April 2025.

The institution also mentioned in the research report that for U.S. stocks, which are at historically high valuations, if the "130-day complexity indicator" based on the relative price ratio of the NASDAQ Composite Index vs. 30-year U.S. Treasury bond prices breaks 1.30, it will indicate a very high risk of a decline of up to 20% in U.S. stocks. BCA Research currently estimates this indicator value to be around 1.37, very close to the critical point. With European and Chinese stock markets continuing to rise recently, the three major U.S. stock indices have been declining, especially the NASDAQ, which has fallen over 5% in the last five trading days. More and more investors are worried about a bear market in U.S. stocks similar to the "internet bubble burst."

How should investors prepare for a potential 20% drop in U.S. stocks? BCA Research suggests that cautious investors should underweight technology stocks (referring to the entire IT sector in the U.S. stock market), overweight the "healthcare" sector, and long-term U.S. Treasury assets, which traditionally have defensive attributes. They also recommend hedging potential downside risks by going long on the volatility index (VIX) or buying put options on stock indices.

It is understood that BCA Research proposed the so-called "Mandelbrot Fractal Dimension" theoretical framework in this research report and cited this theoretical framework to quantify the so-called "complexity indicator," further exploring investment strategies for the global stock market in the near future. The core logic of this report from BCA Research is that the end of market trends stems from a complete collapse of complexity, rather than the emergence of new narratives; it is currently necessary to closely monitor the changes in the fractal dimension indicator, especially the 130-day complexity quantitative indicator of the NASDAQ Composite Index and 30-year U.S. Treasury bonds.

In the view of BCA Research's research team, the so-called "Mandelbrot Fractal Dimension" is a mathematical tool for measuring the complexity of price trends, used to quantify the "information richness" of market trends, or the so-called market "complexity." BCA Research stated that monitoring the collapse of price trend complexity (information richness) is an effective way to identify market vulnerabilities, with the best measurement indicator being the complete collapse of the Mandelbrot Fractal Dimension Generally speaking, when the complexity of price trends collapses, it indicates that too many value investors have fallen into the "purely narrative-driven trap trend," leading to a short-term investment perspective driven purely by momentum and animal spirits, forming the so-called "market vulnerability" concept. At this point, the trend may completely reverse due to a lack of new buyers. In a state of extreme vulnerability, when value investors attempt to exit, they find only deep value investors remaining as counterparties. At this time, trades can only be made at significantly different price level benchmarks, which can trigger a comprehensive market crash. The end of a trend often lacks an exciting narrative, fundamentally due to reaching the limits of market vulnerability.

BCA Research mentioned in its report that the information richness of price patterns comes from: 1) deep value investors - providing structural valuation information; 2) medium-term value investors - transmitting economic cycle information; 3) short-term pure momentum and animal spirit investors - reflecting market sentiment fluctuations.

When the above three types of investors form a balance, the market exhibits the characteristic of "anti-fragility," which is conducive to bullish momentum. However, when value investors collectively shift to momentum and animal spirit strategies, the complexity dimension collapses, and the system enters a vulnerable state, with the next step being vulnerability triggering a comprehensive market crash.

In summary, the "260-day complexity indicator" of the MSCI AC World Index calculated by BCA Research shows that a sell signal was triggered on October 18, 2024 (threshold 1.25). BCA Research stated that this signal indicates that the vast majority of global stock markets will enter a consolidation and fluctuation period lasting until mid-April 2025.

For the "seven major technology giants in the U.S. stock market," which are near historical highs in valuation, as well as the U.S. stock market where these seven giants hold significant weight, the downside risk may be much higher than that of most global stock markets. BCA Research stated in the report that if the "130-day complexity indicator" of the NASDAQ Composite Index vs. 30-year U.S. Treasury bond prices, that is, the fractal dimension of the NASDAQ vs. 30-year U.S. Treasury bond prices, falls to 1.30 (currently 1.37), it will trigger a decline of up to 20%, which would also technically establish that the U.S. stock market has entered a bear market zone BCA Research stated that similar warning signals appeared before the internet bubble in 2000 and the financial crisis in 2008, and successfully warned of market vulnerabilities before major financial disaster events such as the Great Depression in 1929, the oil crisis in 1973, Black Monday in 1987, and the liquidity crisis in 2018. BCA Research indicated that when the so-called "fractal dimension value" falls below 1.30, it indicates that the relative price trend of stocks and bonds is losing diversity (investor behavior is converging), and the market enters a very fragile pessimistic state.

Therefore, as the U.S. stock market approaches the complexity indicator that triggers a 20% decline, BCA Research recommends that investors adopt a "risk-averse investment strategy," being wary of the risk of further collapse in complexity leading to a sell-off, specifically by underweighting technology stocks (referring to the entire IT sector in the U.S. stock market), overweighting the "healthcare" sector, and long-term U.S. Treasury assets, which traditionally have defensive attributes. Additionally, it is suggested to hedge potential downside risks by going long on the volatility index (VIX) or buying put options on stock indices