I have calculated the expected value and standard deviation for a trading strategy for the financial markets, but think that my standard deviation is too low.
Assume the following:
A trading strategy has the folllowing possible outcome:
probability of winning trade = 50%, win will be $1,500
probability of losing trade = 50%, loss will be -$1,000
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) - is this correct?
If I then put the trade on 100 times will my EV and SD be as follows?
EV = $250 x 100 = $25,000
SD = sqrt(100) x $883.88 = $8,839
hi mathaddict, thanks for your quick response. Your explanation is very helpful and it also makes sense. After one trial the SD should be $1,250 (the difference between -$500 and +$750). I couldn't make sense of the meaning of my $883.88 figure!
Thanks again!
Well, I am glad I managed the find this old thread I posted, as I have got a follow-up question on this. (I do apologise for not checking the forum for 5 years!)
In the example above I assumed that a trade could either be a winner or a loser. I would now like to incorporate scratch trades into the equation.
Can I still use the same formula as above?
I am starting with the same numbers as above, but now assume a 10% chance of incurring a scratch trade, which on average produces a small loss of $100. The possibility of a full losing trade has reduced from 50% to 40%.
E(x)=0.5*1500 + 0.4*-$1000 + 0.1*-$100 = $340
E(x2)=1500^2x0.5 +(−1000)^2x0.5 + (-100)^2x0.1 =1526000
Var(x)=1526000−340^2 =1410400
SD= 1187.60
It seems logical to me that the standard deviation is slightly lower because a portion of the $1,000 losing trades have turned into $100 losing trades.
It would be great if somebody was happy to comment on this. Thanks in advance!