Exploring Power Law Distribution in Stock Market Returns

[Tejay]

Hi All,

After reading some books on how stock market returns are better modeled by a power law distribution, I wanted to play with some data based on this.

When using some software and or doing it myself on excel, I can generate one tail, but not two.

This is what I would like my data to look like;

Does anyone know how to do this?

As you might have gathered, I am well out of my depth here. Just looking to tinker with the data for fun.

 

[jedishrfu]

Welcome to PF!

Here's an article on using power laws in finance with pointers to other related articles which may be a good start:

http://physicsoffinance.blogspot.com/2011/12/power-laws-in-finance.html

There are also several papers on this very topic that you can find via Google that I didn't include here because they may be too technical.

With respect to your question though: Can you describe what you mean by one tail vs two tails? is this a limitation of your data or the choice of parameters for your power law graph?

 

[Tejay]

Thanks for the quick reply.
That article is exactly what I am trying to do.

What I meant by one tail is I can calculate say a graph like this for the positive returns;

But I am not sure of the formula I need to use to get the overall distribution or bell shape.

Even better, if this is called a particular distribution I would prefer to generate the graph in a software package. I downloaded Easyfit 5.5, but the power law distribution produces what I am describing as a "one tail" distribution such as the image above and not like the image in my original post.

Thanks :)

 

[statdad]

Excel is the worst tool available for anything statistical. You could try "R" - a powerful yet free statistical software package. I believe (based on memory from a year or so ago) that there is even a package for R that will aid in generating the type of distribution you want.

 

[blue_raver22]

Hello,

Thank you for sharing your interest in exploring the power law distribution in stock market returns. I can offer some insight into this topic. Power law distribution is a statistical model that has been used to describe the behavior of various natural phenomena, including stock market returns. It is characterized by a long tail on one side, indicating that extreme events are more likely to occur than in a normal distribution.

To generate a power law distribution for stock market returns, you can use specialized software or create your own algorithm in excel. However, it is important to note that the data used must be carefully selected and analyzed to ensure it follows the characteristics of a power law distribution. This may require extensive knowledge of statistics and mathematics, as well as a thorough understanding of the stock market.

I suggest consulting with a statistician or financial expert to ensure the accuracy and validity of your data and results. Additionally, there are many resources available online and in books that can provide guidance on how to generate a power law distribution for stock market returns. I encourage you to continue exploring and tinkering with the data, but also to seek guidance from experts in the field to ensure the accuracy and relevance of your findings. Best of luck in your exploration!