The above is known as the Mandelbrot set, named after the mathematician Benoit Mandelbrot who discovered the fractal phenomenon in nature. Now he is dedicating his research in the financial market. He wrote a book called, “The Misbehaviour of Markets”, which I strongly encourage you to read. I reckon it a prequel to “The Black Swan” and this man has great influence on Nassim Taleb. Mandelbrot reasoned that the financial markets behave in multi-fractal characteristics. Clueless? I am none better. His book covered many issues in finance and to make it easier to digest, I will break it down and focus on one concept at a time. Let’s begin with this:
Some people say that short term trading is risky. Intraday trading is risky. Long term investment is safer. Mendelbrot disagrees with it. He suggested that no matter what time frame, the risk is the same. Hence, a trader looking at an hourly chart is no difference in his exposure to risk as compared to a buy-and-hold investor who look long term. Take a look at the above pictures. The picture at the top left corner is the entire size of the object. The one to it’s right is a 6 times magnification of the part on the object. Notice the second picture also have a small box? The third picture (left bottom) is the 100 times magnification of it. And the fourth picture shows the 2000 magnification of the box in third picture.
So what is the purpose or significance of this? Mandelbrot has explained in the book why the market behaves more like fractals than the normal bell curve that the academics currently adopted. But I am not explaining it in this post. So I am jumping into things a little, hope you do not mind. At this moment you should just take it to be true, i.e. the market is fractal in nature. What Mandelbrot is trying to show in the pictures is that no matter how much you zoom in, the object does not get simpler. It is as complex as before. In his own words, “Proper fractals remain equally complicated at every level of magnification.” In fact, it always retain a certain similarity or resemblance of the bigger entity. This means that the financial markets are equally complicated in a 10 year time frame as well as a 1 min or 1 hour time frame. They look the same too. Hence, the risk does not change with a different time frame.
The following picture shows the animation of zooming: