Standard Deviation on Trades

[options-george]

hi all,
i have come across an issue which I am not sure I have found the right answer to.

Assume the following:
You have a bankroll of $100,000 and are willing to risk 1% per trade - thus $1,000

You develop a trading strategy which you consider to have the following (after all costs):
probability of winning trade = 50%, win will be $1,500
probability of losing trade = 50%, loss will be -$1,000

I am looking to calculate the expected value per trade as well as the associated standard deviation:
EV = 0.5 x $1,500 + 0.5 x -$1,000 = $750 + -$500 = $250
Is the standard deviation equal to $883.88? I used the =STDEVA formula in MS Excel i.e.=STDEVA( 750, -500)

And therefore assuming I could put the trade on 100 times would EV and SD be as follows?
EV = $250 x 100 = $25,000
SD = sqrt(100) x $883.88 = $8,839

I am thinking that I must be understating the SD because after only 100 trades, I am virtually certain to be in profit as $25,000 is nearly three standard deviations from $0.

Can anyone comment whether my calculations are correct?

Thanks in advance!

 

[options-george]

got the answer from a maths forum that I found - i had indeed made an error in my SD calculation which resulted in it being understated, the correct answers are:

E(x)=$ 250

E(x^2)=1500^2 x 0.5 + (-1000)^2 x 0.5 = 1625000

Var(x) = 1625000 -250^2 = 1562500

SD = $ 1250


Thus for 100 trades the SD would be sqrt(100) x $1,250 = $12,500

Thus the chance of being break-even or better after 100 trades would be 97.5% assuming that the results are in fact normally distributed.