How much money can you make on the stock market ?

One question that most people interested in investing would like to know is : how much money can you make on a specific investment? What is the potential ROI  or Return on investment? The answer to this question, for any investment, should be : it depends on your time scale. 

As a genreal rule, as long as the market goes up on the long term, that the longer you hold a position, the longer your potential returns are. Warren Buffet made his money buying early and holding for extremely long period of time without selling. This idea is also valid in the bond market: unless there are special circumstances (yield curve inversion), longer term bonds give better yields than shorter term ones: 2 year bonds will give lower yields than 5, 10 or 30 years bonds. Also, holding a position for a long time provides enormous tax saving benefits. For day trading, on a single trade, you can make more money if you buy and wait 15 minutes instead 1 minute to sell your position. Of course, the size of downturns is also proportional. 

The Shorter the Time Frame, the Higher Are Profit Potential

But what if you make multiple trades during a given time period instead of only one? Is it more profitable to place one trade over half an hour, or three trades during that same half an hour ? 

To answer this question, I would like to ask another question from the famous article How Long is the Cost of Britain. In this article, Mandelbrot explains that it depends on the length of your measuring stick. The smaller your measuring stick, the longer the coast of Britain is because you will be able measure more closely the jagged features of the coast. There is no limit to this, so as long as you can use a smaller measuring stick, you will find that length of the coast of Britain keep increasing.

The same phenomena is true for markets. Imagine for the purpose of this demonstration that a perfect machine is able to long and short at the exact moment the market changes direction. The amount of profit this machine would be able to generate will tend to increase as the time frame size decreases. Below is a simple example based on real time data. The potential profit is calculated as the absolute value of the difference between Close prices. From the hourly, to 30 minutes, to 15 minutes, the potential profit goes from 3.75, to 4.25 to 9.25.

    • Hourly time frame: 3.75 
    • 30 minutes time frame : 4.25
    • 15 minutes : 9,25





This idea might be easier to vizualize with graphs. 


This is not trivial. When traders are in a losing streak, they tend to overtrade and place more and more bets. As we can see, more bets on a shorter time frame can generate exponentially more gains and losses. As judgment during losing streaks goes down, this exposes the trader to lose a very high amount of money in a short period of time. 

Fractal Dimension for Stock Markets

In stock markets, the Fractal Dimension is a metric that can be used to measure the degree of  chaos or "choppiness" of the market. The closer it is to 1, the closer it is to a straight line, therefore in theory, the easiest it is to trade. Higher values tend to show markets that are very choppy and mean reversing. 

The calculation of the fractal dimension is a bit complicated and is beyond the confines of this article.

Here are examples of low fractal dimension values. These days tend to be trending.

In contrast, days with high fractal dimension tend to be very choppy and mean reversing. These days are very hard trade.


The choppiness of the market is observable relatively early during the day and seems to be fairly consistent throughout. Therefore, the usage of fractal dimension could be considered as an extra tool in the arsenal of any trader.

Conclusion

These two examples show some fractal characteristics of markets. We are conscious that in this article, we haven't provided concrete applications of the theories on practical cases. Nevertheless, we felt the need to share them as they can be used as building blocks for the elaboration of a successful trading system.



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