![]() It is worth-disclosing that we, at BBSP, add our proprietary touch to the formula when analyzing markets, and that what we are presenting below is the work of the highly regarded Mandelbrot. Access to the revised results of Mandelbrot's studies is hard, however, he did mention that he had better results than other measures, notably such as auto- correlations analysis. Thus, the Rescaled range was developed to test these properties. Mandelbrot, a pioneer of the famous chaos theory that itself englobes the notions of fractality, auto-similarity, among other mathematical terms noticed that these properties could be applied to financial markets and spe cifically to stock market returns. Essentially, the function compares the diffusion of a time series to that of a geometric Brownian motion and identifies if the data possesses auto-correlation i.e. Mathematically speaking, the Hurst exponent revolves around the idea of using the variance of a log price series to determine diffusion. H ow do we get to financial markets from this?Ī f inancial time series has one of three characteristics: trending, mean-reverting, or simp ly a geometric Brownian motion.Ī quick and easy way to know which of the three characteristics is valid at a given moment is through the Hurst exponent, developed by Harold Edwin Hurst while studying the optimum dam sizing for the Nile river in Egypt. Another famous example of a fractal figure is the Sierpiński equilateral triangle.Īlso, i t's worth mentioning that a fractal figure is not necessarily perfect but whereby a visible similarity can be detected. We can notice its fractal elements with the similarity and auto-correlation between its different levels. Consider the most basic example a snow flake. It can also be stated that fractals are simply patterns within patterns which look alike. But what is a fractal?Ī fractal is a figure that is inside another figure and shares the same statistical properties as the former. Mean reversion is the simplest example, fractals being the most evolved and accurate representation of financial markets. ![]() Markets are fractal in natureįinancial markets reflect human behaviour, and to a large extent human behaviour can be modelled using algorithms that reproduce what is commonly found in nature. Mathematicians and psychologists have made major contributions to economics and financial markets and as true believers at BBSP, we are thankful to them for finally closing the long-dated, sterile debate between randomness and determinism in the financial markets field, or for at least taking it to another dimension. ![]() A time when only economists could be awarded Nobel Prizes in Economic Sciences has been over for decades.
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