# Expected Value / Statistical Variance / Monte Carlo Simulation Problem

#### Raph

##### Junior member
19 0
Hi everyone. I am trying to figure out the expected value for a hypothetical stock market trading system. I don't know if this question falls under basic algebra, or statistic, or what, but here is are the inputs:

Size of average profit: \$2000 (10 times larger than the average loss)
Holding time / length of average winning trade: 3 days
Size of average loss: -\$200
Holding time / length of average losing trade: 1 day
Total number of investable / tradable opportunities (entry signals) per year: 126
Percentage of trades that make a profit: 40%
Percentage of trades that incur a loss: 60%

Extra info:
All profits are reinvested seeking compound growth.
Total risk per trade: 3% of total capital (adjusted constantly to remain at 3%).

What would be the expected value of such a trading system for every one-dollar put at risk?

And if you have time... is there an excel formula I can use to create a spreadsheet for the data (assuming we start with a balance of \$10,000)?

Thanks!

Last edited:

#### Shakone

##### Senior member
2,458 665
lol! the stats are 100:1 reward to risk with a 40% prob of winning lucky you.

Expected Value = Prob(winning)*(Size of average win) - Prob(losing)*(size of average loss)

Yes there is an Excel formula you can use.

In fact, I think on second thought we should take account of the time-value of money, so

Expected Value = Discount factor*[Prob(winning)*(Size of average win) - Prob(losing)*(size of average loss)]

If you're assuming a stochastic discount process, I can give you the Feynman-Kac generated PDE.

#### Raph

##### Junior member
19 0
lol! the stats are 100:1 reward to risk with a 40% prob of winning lucky you.

Expected Value = Prob(winning)*(Size of average win) - Prob(losing)*(size of average loss)

Yes there is an Excel formula you can use.

In fact, I think on second thought we should take account of the time-value of money, so

Expected Value = Discount factor*[Prob(winning)*(Size of average win) - Prob(losing)*(size of average loss)]

If you're assuming a stochastic discount process, I can give you the Feynman-Kac generated PDE.

Well, I know the formula for calculating expected value, but the fact that the winning trades are held longer than the losing trades is what's confusing me - I was trying to adjust the formula for that. I don't think the "discount factor" will help with that because I am not factoring interest rates. I am guessing that the (hypothetical) system I have come up with will result in approximately +/-20 winning trades per year, and around +/-65 losing trades, but I suck at math so I am attempting to run some simulations. Anyway, I did find a excel based simulator on another forum, and while it's not accurate it's given me some direction. Thanks for your input.

#### Raph

##### Junior member
19 0
Yes, I think there's a 0 missing from the average loss - otherwise you had the Holy Grail .

The expected value is annual return divided by initial capital. The difficulty lies in determining the initial capital.

The usual way is calculating the maximum drawdown with a Monte Carlo simulation from an equity curve _without_ reinvestment. The initial capital is then the maximum drawdown plus the maximum margin, normalized to 3 years.

Indeed you are correct, lol! There WAS a zero missing, and it's been corrected. Though still a pretty impressive system I'd say =p Then again, you know how it is... these kinds of ideas usually just look good on paper, lol.