J200 and Normal distribution

This graph represents distribution of difference of daily prices at market close (in percentage terms).

Simply put, I’ve calculated how today’s close compares (in percentage terms) to previous day’s close. Data is for Top40 (J200) and it was calculated from 05.02.1996 – 05.02.2010 (total of 3440 trading days).

Attached table shows what the values for daily return (mean) & standard deviation of daily returns are and I’ve included values up to 6 standard deviations from the mean.

Finally, third table is just there to give us basic information on what various standard deviations beyond the mean are for normal distribution. (For more information on normal distribution, among other sources, I would recommend Wikipedia.)

It is obvious that our market is not normally distributed. This leads me to conclude the following:

If market is not normally distributed, than simple trend following system (derived from technical market observations) will produce results that are not normally distributed.

For more reading on daily distribution of US Markets, please read the following:

http://marketsci.wordpress.com/2008/10/27/fat-tails-normal-distributions-random-walks-and-all-that-jazz/

http://ibankcoin.com/woodshedderblog/2008/10/26/on-fractals-and-market-crashes-part-1/

Trade with trend!