rate of returns - fit with Normal? Goodness of the fit?

[arabidze]

Hello,

sorry for stupid question, I'm a bit new to all this..

I want to check the distribution of rate of returns, on some Stock price. In text books, its always assumed that the rate of returns is Normally distributed (plz correct me if I'm wrong).

For a given Stock, if I build a histogram of x = (final_price -initial_price)/(initial_price)
shall I try to fit it with the Normal distribution? Shall I expect a good fit?

I took daily stock price of BAC and have built the histogram for rate of returns, for 7'166 days.
If I fit it with Normal distribution, Chi2 test gives me almost zero probability ...
(error at each bin = sqrt(bin content))

Any suggestions?
Thanks!

 

[mhy]

Typically stock returns are symmetrically distributed but with fatter tails on both ends than a normal distribution. You can try a t-distribution which would have fatter tails. There are tools in R / Matlab that allow you to try various models, and even some libraries that will do the determination for you (i.e. it will choose a well-fitting model)

 

[yetanotherquant]

Hello,

sorry for stupid question, I'm a bit new to all this..

Asking may mean one minute embarrassment.
Not knowing is a lifetime shame
(Chinese proverb)

In text books, its always assumed that the rate of returns is Normally distributed (plz correct me if I'm wrong).

There are also enough textbooks in which the non-normality of stock returns is exhaustively discussed.
The normality assumption is mostly to find not in [modern] books on empirical finance but rather in the beginner books on option pricing. As a matter of fact, this assumption allows constructing a very nice option pricing theory.
There are also enough books on Levy models (capture nonnormality).

However, the normality assumption is not unrealistic, at least if you cut tails.
In many cases engaging more complicated distributions makes your model much more complex but brings little in practical terms, esp. if you model in long-term.

Have a look at my book: http://www.yetanotherquant.com
You will find useful info on returns normality and independence, volatility clustering, etc.

 

[Jamal Munshi]

you may use the chi-square normality test.
you can do that on excel.
here is an online tutorial i made a while ago.
hope it helps.

 

[Ken Abbott]

Do a Q-Q or a KS.