200%/year for an AVERAGE trader according to Acrary, still true?
- Thread starter shortie
- Start date
I can't understand one small detail in the report. I've seen it in the "systems development" thread too.
The report at the bottom says:
"Expected outcome 346,190.63"
Shouldn't the expected value be at the 50th percentile of sorted Monte Carlo simulation results?
It's "50% level 323,097.59"
Seems like the expected outcome is taken from around 55th percentile. Why this optimistic bias? Not that it's hugely important, but I'm interested in your reasoning.
I was curious about that too so I tried to duplicate acrary's results. I got close but am not 100% sure it's right (and it's late). Maybe acrary will stop back in tomorrow and let us know.
What I think causes the difference is the drag effect caused by fixed fractional betting (that acrary described a while ago and that I had never really taken a look at.) The expected outcome is a calculated number, not an output from the monte carlo, and in essence, I don't think it experiences the drag since it is only summing positive results.
When I reran the simulations using a percentage of starting capital instead of a percentage of current capital to size the positions, the expected outcome matched the 50% level from the monte carlo.
It's like anything else in life, most people just talk about it but can''t really do it. I guess that's why I hold professional athletes in such high regard, I actually can witness their greatness, it's not some bullshit sales pitch.
I could try this experiment too. But there's one thing unclear to me. There are average winning trade and average losing trade sizes specified. I bet he assumes normal distribution, this means you need to know standard deviation to simulate these variates. I'm quite sure deviation doesn't affect expected profit factor, but my bet it would relate to dispersion of sorted monte carlo results (not the 50th percentile though).
There also another technical detail. What to do if you draw negative "winning trade" or positive "losing trade"? For instance:
you draw standard normal value of -1.5, if mean is 200 and standard deviation is 200, that makes 200 -1.5*200 = -100. What do you do? Ignore and re-draw again? If so, you won't get a normally distributed variable with specified parameters. You would get chopped off, skewed to the right distribution.
I didn't use a normal distribution for the trade draws. I used binary outcomes (if you win, you win this much, if you lose, you lose that much). I took his average profit, average loss, and win percentage only as a description of the profit factor. I'll post some pseudo code describing what I did. If you implement something using normal draws, let me know what you find.
First I found the win to loss ratio. With 50% wins, that is equal to 1.5 (the profit factor). More generally:
winLossRatio = profitFactor * (1.0 - percentageProfitable) / percentageProfitable;
To calculate the expected outcome:
balance = startBalance;
for each trade
{
risk = balance * tradeRiskPercent;
reward = winLossRatio * risk;
result = reward * percentageProfitable - risk * (1.0-percentageProfitable);
balance = balance + result;
}
To calculate each monte carlo run:
balance = startBalance;
for each trade
{
risk = balance * tradeRiskPercent;
reward = winLossRatio * risk;
isProfit = nextRand(0, 1) < percentageProfitable;
if(isProfit) result = reward;
else result = -risk;
balance = balance + result;
}
