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November 18th, 2011, 08:35 AM   #1
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Trading system probability problem

This is a question for those good at probability. It has to do with probability distribution and probability mass function. I'm a programmer but I'm not very knowledgable in those fields.

Now, let's say we have two trading systems which buy and sell stocks; System1 and System2.
Each places trades (buys/sells) for 5 days and these are the end of day profit results for each day:

System1:

1: +210
2: +90
3: +20
4: +70
5: -340

Total System1 = +50
Average daily = +10

System2:

1: +20
2: -10
3: +15
4: -5
5: +30

Total System2 = +50
Average daily = +10

--------------------------------

On the face of it, both systems are equally profitable. However, the price distribution on system1 is much wider than system2, indicating
there was an element of luck involved. This means that the true profitability (predicted forward) of system1 should be lower than system2,
if we were to adjust according to the risk and unreliability of the results.

I am using only 5 days for the sake of simplicity, but sample size will be a constraint in real testing also.

Questions:
-What is the probability that the next (6th) day will be +10 (average daily) for system1 and system2?
-I expect that it will be higher for system2 and lower for system1. How would I calculate exactly by how much?
-Is calculating the probability of the average daily a good measure of how risky the results are, so that i could arrive at one score by multiplying the calculated probability with the average daily to arrive at a uniform scoring method for each of the systems? If not, would you suggest another method to arrive at a unified scoring system (ie risk aversion variable)?

I'm not super great with formulas, i'm a programmer trying to make sense out of stuff. If anyone would explain to me the solution in a procedural (code-like or understandable) way, I would greatly appreciate it.

PS
I'm not even sure i'm approaching this problem correctly, or that it has so much to do with probability. Maybe i'm just using the wrong formulas.

Thanks.
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November 18th, 2011, 09:08 AM   #2
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Re: Trading system probability problem

After thinking about this a bit more, i'm not so sure it's a probability problem. Maybe it's a risk (of loss) aversion problem?

If it can be confined to a probability problem, i'm very happy.
If it's a risk aversion problem, i'd like suggestions as to how to quantify it mathematically.

Thanks
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November 18th, 2011, 10:17 AM   #3
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Let me rephrase the problem

Ok, let me rephrase the problem.

There is the Sharpe Ratio.

Sharpe Ratio = sqrt(250) * (AverageDailyProfits / StdDev(ProfitSeries))

I am trying to find a system that will, over time, not have major losses.

My concern is that if i score systems like this:

Score = AverageProfits * SharpeRatio

My scores will not be linear compared to the AverageProfits if i plotted the curve as a function. This is because Standard Deviation is not linear. My concern is that i would have some systems with higher average profits loose out (in the score) because their sharpe ratio is only a little bit lower. Due to the non-linearity of it, "little bit lower" means lower enough to have a lower overall score.

My question now becomes:

Is there a mathematical way to counteract the non-linearity of StdDev?
Can I multiply the SharpeRatio by some function to remove the non-linearity?

Thanks for your time.
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November 25th, 2011, 12:07 AM   #4
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Re: Trading system probability problem

May I ask why you're asking this? Are you doing this for fun or for a project. Or are you trying to do this as an actual trader?
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