Trade Smartly in the Fractal Stock Market with Machine Learning Power

motek 1This algorithmic article was written by Yutong Li – Analyst at I Know First, Master’s candidate at Brandeis University.

Fractal Stock Market


  • Although Efficient Market Hypothesis has been a dominated financial theory for years, it fails to give a sensible reason and interpretation of the financial crashes and crises that occurred
  • A more comprehensive financial theory – Fractal Market Hypothesis is capable to explain these crises and provide a clear-cut description of the financial markets
  • Fractal Market Hypothesis puts forward the idea of self-similarity and stability in the market when it consists of investors from a wide range of investment horizons
  • FMH verifies the root of technical analysis under the idea that history can repeat, and this process of pattern-finding can be efficiently attained by machine learning

Efficient Market Hypothesis in the Context of Financial Crisis

Efficient Market Hypothesis

For years, the Efficient Market Hypothesis (EMH) has been a dominant play in financial theories on markets. EMH proposes that investors are acting rationally, and the market is efficient in the sense that share prices can reflect all information at their fair value. The theory also posits that investors are unable to outperform the market or obtain consistent returns as they have the same amount of available information efficiently distributed by the financial market. 

While EMH has remained as a leading edge in financial conjectures, Robert Shiller, a famous economist, insists that the volatile nature of asset prices can lead to a violation of EMH in terms of market efficiency and rational expectation. More notably, the 2008 financial crisis has again questioned this mainstream framework. According to EMH, such a crisis would not exist since this type of economic bubble occurs when asset prices deviate from their true economic value, and this has contradicted the main idea of EMH. 

Fractal Market Hypothesis – A Comprehensive Framework

Due to the global financial crisis, EMH was again challenged. The question was raised surrounding whether there is a more comprehensive theoretical framework or a better explanation of the crisis and turbulence in the stock market than EMH. Fractal Market Hypothesis (FMH), as an alternative investment theory, can offer some answers to this question. 

Benoit B. Mandelbrot was a mathematician universally known as the father of “fractals” and introduced the phenomenon of “fractals” or “self-similarity” in geometry which refers to a fragmented shape that can be broken down into smaller parts with similar shapes. From the below graph, we can see this central idea of FMH, self-similarity, being presented. And in 1991, Edger Peters explained Fractal Market Hypothesis within the framework of chaos theory in his book “Chaos and Order in the Capital Markets“. According to Fractal Market Hypothesis, financial markets tend to follow a stable and cyclical pattern, and history can repeat itself. 

Fractals in Geometry

More specifically, to ensure the stability or self-similar trait of the stock market, Fractal Market Hypothesis puts a heavy emphasis on investment horizons, the liquidity of markets, and the role of information. Let’s first take a closer look at these fundamentals of FMH (according to Investopedia) and examine how financial crises can be well explained by FMH. 

Fractal Stock Market: Fundamentals of FMH

Investment Horizons

Investment horizon is defined as the time length that investors expect to hold their assets and can reflect investor’s degree of risk exposure and their investment strategies. By FHM, the dominance of one investment horizon would weaken market liquidity, and thereby cause the instability of the stock market. Going back to our example of the financial crisis, when long-term investors see prices fall during the crisis, they are likely to shorten their investment horizon, which causes an imbalance when short-term trading activities outweigh long-term activities. As a result, the market is more inclined to a less liquid and unstable state.

Market Liquidity

Market liquidity refers to the efficiency with which an asset or security can be bought and sold at stable prices, and it is generated when two investors hold different positions or values on the asset or security. During the time of a financial crisis, many long-term investors reduced their investment horizons, and fewer people are willing to take the other side of a trade. Subsequently, market liquidity would dwindle.

Fractal Stock Market Liquidity

The Role of Information

Based on FMH, the role of information is critical since it can determine the decision of investment horizons and market liquidity. In times of stable markets, investors share the same information, but the way how they interpret the information may vary. For instance, a day trader may sell the asset due to short-term price volatility, and on the other hand, a pension fund manager may tend to focus more on the long-term growth and ignore the price turbulence in the short term. As we just discussed, this variety of investment decisions can lead to market liquidity.

Nevertheless, in the context of a financial crisis, when long-term investors observe major declines in the stock prices, they may lose confidence in their investment decision and begin to short. And this type of decision-making is affected by human emotions and biases, as evidenced by the idea of Behavioral Finance. When the market does not have a wide range of investment horizons and perspectives, this will lead to a less liquid and shaky market.

Fractal Stock Market: The Role of Information

Altogether, Fractal Market Hypothesis emphasizes the significance of different investment horizons, market liquidity, and the role of information in ensuring market stability. The financial crisis can now be explained by the fact that some investment horizons shorten, short-term information dominates, and market liquidity is reduced. Hence, the market is no longer stable.

Fractal Market Hypothesis in Trading 

According to Investopedia, fractals are defined as recurring patterns that are composed of five or more bars. As shown in the below graph, the left fractal indicates a bearish position when there is a pattern with the highest high in the middle and two lower highs on each side, and on the other hand, the right fractal presents a bullish signal as the pattern shows the lowest low in the middle and two higher lows on each side. Following this law, traders can expect a price increase after observing a bullish fractal, or a price drop following a bearish fractal. 

Fractal Stock Market

Does this type of analysis look familiar to you? You may think that this looks much like technical analysis which also navigates price patterns using the historical price to facilitate investment strategies. More essentially, Fractal Market Hypothesis confirms technical analysis under the central idea that history can repeat. Fractals are also widely used in conjunction with other technical indicators such as moving averages to explore price patterns. 

In accordance with the idea of FMH, technical analysis has the exact same conjecture that history tends to repeat itself, and therefore by analyzing the price trend in the past, future price movements can be predicted and more accurate investment decisions can be made. All in all, we can see this central premise of FMH has been prevalently utilized as a solid buttress in technical analysis and makes it easier for traders to understand the market prices and react cleverly. 

Furthermore, according to this article, one striking thing to note is that this idea of “fractal” or pattern-finding can also be realized by machine learning. What’s more, not only can machine learning find patterns just as technical analysis does, but also it can explore the trends in a more automated and efficient way through training, validation, and testing. Additionally, this article also points out more advantages of machine learning that can outdo technical analysis in terms of finding patterns and providing trading insights. For example, machine learning can avoid human bias, it can provide a competitive advantage if a good model is built and used, and it can take external factors into account and guarantee extra accuracy, etc. Therefore, the core of FMH and technical analysis can be perfectly fulfilled by applying machine learning. And machine learning can ensure reliable and well-grounded investment decisions in financial trading.

I Know First’s Machine Learning Algorithm

I Know First's algorithm

I Know First is one leading company that has been effectively using machine learning and AI-based algorithms to provide daily forecasts and facilitate trading for over 10,500 financial instruments. More importantly, I Know First’s algorithm can fulfill the idea of discovering “fractals” and patterns using a more accurate way through AI and machine learning without involving any human judgments. The algorithms can present historical price patterns based on the data inputs, testing the performance on years of market data, and validating them on the most recent data to prevent overfitting. If an input does not improve the model, it is “rejected”, and another input can be submitted.

I Know First’s algorithm has also achieved notable success as shown in the below forecast performance report for the most recommended investment avenues for the first half of 2021. This report was published on January 7th, 2021, and contains a broad range of forecasts for financial assets in 6 months ahead including stocks for the US market, European market, ETFs, Commodities market, Currency and Cryptocurrency markets. Among all the recommended forecasts, I Know First’s algorithm has correctly predicted the price movements of 30 out of 36 assets and the overall average return has obtained 24.36%, outperforming the S&P 500’s return of 12.98% with a market premium of 11.38%. With this excellent outcome presented, I Know First’s algorithm can be considered as an expert player in finding patterns and trends and making investment decisions more reliable and accurate.

I Know First's algorithm


In a nutshell, we can see that the conventional Efficient Market Hypothesis fails to hold when it comes to the financial crisis. Alternatively, Fractal Market Hypothesis delivers a more comprehensive framework of financial markets and can explain the cause of the financial crisis in terms of the fundamentals – investment horizons, market liquidity, and information. In addition, FMH asserts that the market is stable and price series are self-similar when the stock market is liquid, holding a combination of short and long-term investors. Besides, the central idea of FMH – patterns are repeatable, is also in consonance with technical analysis. Fractals can be used in conjunction with other technical indicators to facilitate better trading ideas. More importantly, machine learning can serve as a more automated tool than technical indicators in terms of pattern finding, and make people trade smartly in the fractal market with more efficiency.

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Please note-for trading decisions use the most recent forecast.