Thread: Standard Deviation on Results of Stock Trades

Originally Posted by george12345

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

I agree with your expected value but not the standard deviation.

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

The last part is correct after you modify the SD.

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!

Originally Posted by george12345

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!

That's the SD of -500 and 750.

What you are asked to calculate is the SD of the grouped data

X ............... P(X=x)

-1000 ............... 0.5


1500 ................ 0.5

Of course, you are welcome.

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!