# probability on strategy expected return

I’ve been thinking about this for awhile and couldn’t figure it out myself.

Assume you have a trading strategy, which return is normally distributed. strategy return has a mean of 1 basis point and a standard deviation of 20 basis points. Now, how many times do you have to run this strategy so there’s a 99% chance you don’t lose money (your expected return is 0) ?

I understand that if returns are normally distributed , then from Z score I can calculate the probability of any return. However that doesn’t solve the above problem...

• Are returns multiplicative or additive? Zero times is one answer ;) Mar 30 at 8:09
• Set up the problem in Excel and try it out yourself! You can use Monte Carlo simulation to answer your question. Generate a bunch time series of random draws using RAND() and NORM.DIST. Then in the final column, use COUNTIF() to see how many of your time series are above 0 at every time step. If you do 10000 time series, look for where your COUNTIF shows 9900. Mar 30 at 11:19
• @BobJansen that’s true! Mar 30 at 11:34
• It does make a difference whether returns are multiplicative or additive though. Mar 30 at 12:01
• By Cantelli's Inequality, if you run it 40,000 times (!) for additive returns, the mean is 40K bps, and the standard deviation is 4K bps, so the probability of a loss is smaller than $1/101$. This is covered in chapter 2 of Short Sharpe Course. Mar 30 at 16:31