- Say that there's a probability p of making one unit of P&L (e.g. 1 tick = 1 cent) and a probability 1-p of losing the same amount of money
- Draw n samples of a Bernoulli distribution with probability p, subtract 1/2 and multiply by 2 to get a coin toss mapped into the P&L distribution above (edited: subtract 1 => subtract 1/2, noticed by P Fermat; the notebook used 1/2)
- Let's have n equal to something like 7*60*x, where we have x trades every minute over 7 hours of trading
- We then accumulate the P&L (assuming no further risk measures that would stop trading if the accrued loss was too high) for each run.
- We look at the distribution of accumulated P&L to estimate how many losing days such a trader would have

If we have p equal to approximately 52.5%, and 10 trades per minute, it looks like this trader would have one losing day every 8 years.

A PDF of the Mathematica notebook is attached. Download Virtu

In step 2 it should be subtract 1/2 instead of subtract 1, right?

Posted by: P Fermat | April 03, 2014 at 09:28 PM

Yes, either multiply by 2 and subtract 1 or subtract 1/2 and multiply by 2; the notebook has the correct calculation.

Thanks for the comment, I'll edit the post.

Posted by: Marcos Carreira | April 03, 2014 at 10:26 PM