I’ve been trying to wrap my head around a few new theories and concepts I’ve been developing for a while. I recently saw a PBS show discussing Mandelbrot fractal mathematics and it immediately occurred to me that this could be the missing link from what I’ve been trying to figure out. If you need a quick primer on fractals, I suggest you click here for a quick and easy description.

Fractals are easy to see in geometric form and occasionally in living creatures and throughout nature when paying close attention. What is not so easy to see are fractals in finance. For those who read this blog frequently, I have a sister website that deals with trading options on Exchange Traded Funds over at ETFCoveredCalls.com that has done fairly well for me over the past few years. I have consistently been able to extract about a three percent monthly return in cash flow from the financial stock markets over the years but I’ve been trying to automate the entire system and give myself an edge as the markets and technology evolve.

The key formula(s) I am trying to develop revolve around using integration to find certain ranges and limits to certain financial markets parameters. I’m not necessarily interested in finding an absolute answer but rather understand the “surface areas” and limits of the monster curves in the subsets. This would involve integrating various calculus functions as seen here, with Mandelbrot’s fractal theory.

In my investment world, I see investors buying or selling various investments such as ETFs, Stocks and/or Options amongst a variety of things. Each of these three particular items (which I focus on) contain a “recursive self-identity” to them that I haven’t been able to formulate mathematically. You can review these primitive graphs to try to visualize what I’m discussing.

FractalFinance1.png

In the picture above, you have investors that buy/sell various investments.

FractalFinance2.png

In the second picture above, if an investor has chosen to invest in an ETF, there are various things he could potentially do such as trade options on that particular ETF. The “fractal recursion” however becomes interesting when you consider that ETFs are essentially a bundle of stocks.

FractalFinance3.png

In the last image above, when we consider ETFs and understand that they are made up of individual stocks, we determine that these individual stocks have a subset of derivatives (options) which can be bought/sold as well to investors.

The buying/selling of options, leads to the buying/selling of stocks, which leads to the buying and selling of ETFs. You can “drill” up and down the path and see a superset or subset of derivatives depending on where you are but they are almost self-identical.

Why am I pursuing this? Because ETFs are relatively new and the ever evolving markets require bleeding edge thinking and research. I’ve never been content to simply “set it and forget it” buy purchasing index funds and hope for the best over the next 30 years. The economic turmoil in today’s world is an indication of the intricate nature of how markets are evolving. I think we’ll find ourselves far detached from the old days of “set it and forget it” fairly soon if we haven’t already.

Besides, I’m fairly bored too ;)