I wondered what would happen if you had perfect predictions about a stock and added noise to them, how bad your predictions needed to be to kill your profits?

Heres how it works:
First note: a buy order placed today, will be executed at tomorrows close.

1) Use Quandl to get tomorrows price and the price for the day after
2) Use these to predict the return if an order was placed today
3) Add some zero mean Gaussian noise to the return to simulate prediction errors
4) If the predicted return is bigger than some minimum value, minreturn, buy 100 shares
Similarly if the predicted return is smalller than -minreturn, short 100 shares

Quantities to vary:
sigma - amount of noise: 0.0 = perfect predictions,
0.5 = mostly noise
minreturn - minimum return to initiate buy: 0 = buy more often but have commission losses,
0.02 = buy only when predicted daily return greater than 2%

When minreturn=0.01 (i.e. greater than 1% predicted daily return required to initiate buy),
three random samples were:
sigma = 0.00001, returns = 55.9%, 55.9%, 55.9% (Perfect predictions)
sigma = 0.01, returns = 51.3%, 50.8%, 51.3%
sigma = 0.05, returns = 22%, 25.1%, 22.8%
sigma = 0.1, returns = 12.6%, 14.29%, 11.9%
sigma = 0.5, returns = 3.5%, 3.2%, 3.4%
As expected increasing noise, reduced profitability.

Has anyone modelled their real predictions? Are they correlated? What mean/stdev are they?