Feb

28

Fractal scaling and the aesthetics of trees

Trees in works of art have stirred emotions in viewers for millennia. Leonardo da Vinci described geometric proportions in trees to provide both guidelines for painting and insights into tree form and function. Da Vinci’s Rule of trees further implies fractal branching with a particular scaling exponent.

H. Humbert writes:

I could never understand how fractals help with markets. Yes, the world is fractal, but fractals are essentially a way to describe the "roughness" of random patterns. But is this roughness permanent? No. Are the patterns predictable? No. Yet somehow some wiggles are described as bullish and bearish fractals. Sounds like snake oil to me.

Asindu Drileba responds:

You're right! Mandelbrot himself admits that his techniques cannot predict the direction a financial instrument will move. He however says that his techniques can predict "by how much" a financial instrument will move. He describes that "large movements are more likely to be followed by large movements" and "small movements are more likely to be followed by small movements." Here is a short video of Mandelbrot describing his model.

H. Humbert replies:

Never read his books. I know Victor hated him with passion, he was one of the three most guilty, the other two were Taleb and Buffett. Watched the video, a lot of words but nothing practical. Also since his mode of thinking is simple and algorithmic, and he is famous, if there ever was anything to be gained from it, by now algorithmic trading surely made all those possible gains disappear.

Laurence Glazier comments:

There is always an element of hand-waving in attempts to make things easier than they are, and it can be seductive. Nature, however, likes economy of means, and therefore if the same-ish pattern can be used at different scales, I would expect this to happen - but this assertion itself has an element of hand-waving.

H. Humbert adds:

To me the main element of hand-waving is that coastal topography and tree branch patterns created by very different mechanisms themselves have anything to do with predicting market moves where human psychology among many things is involved.

Zubin Al Genubi writes:

There are entire financial industries and degrees relating to prediction, measurement, and trading volatility. It is one of the most important aspects of trading and protecting yourself from ruin. A simple example of the importance of understanding volatility is its mean reversion. In time of stress and price drops this is a key.

Anatomy of a Meltdown: The Risk Neutral Density for the S&P 500 in the Fall of 2008, Justin Birru and Stephen Figlewski.

September 2008 was when the crisis hit in force….On 55% of the trading days in October and November 2008, the index moved more than 3% up or down (corresponding to annualized volatility in excess of 47%). Interestingly, while it is well-known that the market tends to move faster and further on the downside, in this extraordinary period sharp moves to the upside were just as common. On the two days with the largest price changes in October, the market rose more than 10%.

H. Humbert continues:

Once again something unpredictable happened that was difficult to take advantage of. It seems like crisis-related volatility would have to subside sooner or later when the crisis is over, is this a revelation? I recall the March 2020 day when the market hit the Covid lows. I literally said to myself "this has got to be the bottom". But did I do anything? No, because I really wasn't sure. Some forces ended the crisis, but they're only obvious in retrospect.


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