How can I generate a two-tailed power law distribution for 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.