Probability of success due to chance alone?

I thank you for your help and introduction to R value.

After looking on the internet, it seems that:

I can now calculate the Kelly%, the optimal amount I should be trading to maximize profits.

Kelly% = W - (1-W)/R
= 0.64 - (1-0.64)/1.41
= 0.38

According to what I've read, 80% of 0.38 = 0.30 and is what I should be trading to maximize profits or about 30k on a 100k account.

Ironically, this seems to be intuitive since I just don't feel too comfortable risking more than 33% of my equity.

In addition, I can work on decreasing my average loss by not hedging as much.

There is so much to learn.
 
Impossible.

Take an average return of 30%, per year.

Assume 100 trades a month (1200, per year).

Determine your average risk:reward. 1:1.5? 1:2?

Enter your average stop loss (risk). Enter your average take profit (reward).

Plug all that into a Monte Carlo simulator using real market data and see how many iterations it takes to generate the target return. Run that simulation a few times then take the average. That's your ~probability.

As the expected return (reward) increases, performance will decrease commensurately.

Not to say it can't be done. Just not by chance.
 
Quote from anesthesiaman:

I would like to determine the probability of my success being due to chance alone (and thus not my skill).

I started trading futures for the first time on May 25, 2010 (although I also know how to trade options and stock also - so I'm not an absolute beginner).

On a 100k account I'm up a little over $7500. I took the month of Sept 2010 off to study for my anesthesiology oral boards - so this month should not count in the probability determination.
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given what you have described here, I do not see anything in the length of time or the amount you are up to suggest any kind of skill or edge. now if you double your account in 1-2 years, that might mean something.

Also, what are your drawdowns? What is your trading style? how often do you trade?
 
Quote from JoePaterno:

given what you have described here, I do not see anything in the length of time or the amount you are up to suggest any kind of skill or edge. now if you double your account in 1-2 years, that might mean something.

Also, what are your drawdowns? What is your trading style? how often do you trade?
More...

What makes you so certain that my results are due to 100% to chance (i.e. luck?). That's the P value I'm trying to figure out and the reason for this thread. Not just willy nilly - seat of the pants - type analysis (like my trading style). I want to know if the P value of my results is 0.05 or less.

I will repeat: my trading style is completely discretionary, I hold for 1 day to maybe 2 weeks.

My loses actually include hedges too, so it's hard to say what is a real drawdown. Sometimes I make money on the hedge and the actual trade. But most of the time my hedge just gets in the way of pure profitability. And also I sometimes scale in/out of positions. I have calculated a rudimentary R-multiple and a Kelly %.

Here's my problem:
1) I don't know statistics well.
2) I don't know how to determine trades/drawdowns OF INDIVIDUAL TRADES when I hedge and scale in or out (although I do keep a trading journal). But I can calculate based on total amounts (see #4 below).
3) I don't know of a program to analyze my trades from Thinkorswim. Know of one? Should I just download statements and plug them into Excel?
4) I CAN however calculate numbers based on TOTAL AMOUNT PER VEHICLE that Thinkorswim gives me - namely 25 vehicles (futures +/- their hedges) that I've traded with varying losses and wins. I know I've traded a lot more b/c my commissions at TOS are $1100 or so.

The calculations are pretty simple:

W = Win rate = 16 profitable vehicles / 25 vehicles traded = 0.64 = 64% win rate.
Total win = $12558.60 in 16 different vehicles
Total loss = $554.87 in 9 different vehicles
Avg win / 16 vehicles = $784.91
Avg loss / 9 vehicles = $554.87
R = Historical Avg Win/Loss ratio = $784.91 / $554.87 = 1.41
Kelly % = Percent of total capital that should be traded to maximize profits
Kelly % = W - (1-W)/R

80% of the Kelly % should be risked, although I don't know how they come up with 80%.

So, my Kelly % is 0.38. And 80% of this is 0.30 or about $30k on a $100k account.

However, many of my "losses" are from hedges using options. So here's what I need to do: if I decrease this hedging, not only will my win rate increase, but my avg loss / trade will decrease further. In addition, if I can stop selling too soon, I would increase my avg win / trade since after I sell, the vehicles I trade always seem to keep going in my direction.

And it's funny because intuitively I didn't need to make all these calculations because: I don't feel comfortable risking more than 33% of my account; I am working on not selling so soon and missing out on profit; and I've began to decrease the amount I've been hedging because it just seems to decrease my profitability when I often get the direction right anyway, up or down.

In other words, the win rate is probably higher than 0.64, and I need to minimize losses. So really, all these calculations were for nothing, b/c all this makes common sense (maximize gains and minimize losses)! But it at least forces me to think about how and why I can improve.

There is so much to learn...

I do not think my results are due to chance alone. But that is always a possibility even if I doubled my account in 1 year. And so I just want to know WHAT IS THE EXACT PROBABILTY (i.e. the statistical P value) of me just being lucky and that my results of 7.5% return on trading capital (100k account) from May 25, 2010 to August 31, 2010 (with $1100 trading commissions) is due to PURE chance alone and ZERO skill.

Anyone know how to do this probability calculation?

Thanks,
Anesthesiaman
 
25 trades over 3 months is too small a sample to draw any conclusions. conversely, you could have had 19 losing trades and that also wouldn't mean you're a bad trader either.

you need thousands of trades over a few years to know
 
Quote from blackjack007:

25 trades over 3 months is too small a sample to draw any conclusions. conversely, you could have had 19 losing trades and that also wouldn't mean you're a bad trader either.

you need thousands of trades over a few years to know
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Its not 25 trades. It's a lot more. $1100 worth of $3 commission per contract at TOS. TOS just gives me the vehicles I've traded and their TOTAL profit or loss (although each vehicle may have been traded hundreds of times).

I don't know how to get/calculate the individual trades so I just used the total trades in the above calculations.
 
I think what I'm asking if this makes sense to anybody is:

Where on the binomial distribution curve does a 7.5% return in 3 month over 300+ trades lie?

I.e. Is this less than 1, greater than 1 or greater than 2 standard deviations from the mean?

How come I don't know statistics well, yet no one seems to know what I'm talking about or has mentioned anything close to what I'm asking?

Sample size is related to what I'm talking about (I.e. "power" of a study), but NOT a probability. But amongst the universe of futures traders where do my results lie?

I'm talking about inferential, not descriptive, statistics here.

I guess no one knows what I'm talking about. And I certainly dont know enough about statistics to answer the question!
 
Quote from anesthesiaman:

I think what I'm asking if this makes sense to anybody is:

Where on the binomial distribution curve does a 7.5% return in 3 month over 300+ trades lie?

I.e. Is this less than 1, greater than 1 or greater than 2 standard deviations from the mean?

How come I don't know statistics well, yet no one seems to know what I'm talking about or has mentioned anything close to what I'm asking?

Sample size is related to what I'm talking about (I.e. "power" of a study), but NOT a probability. But amongst the universe of futures traders where do my results lie?

I'm talking about inferential, not descriptive, statistics here.

I guess no one knows what I'm talking about. And I certainly dont know enough about statistics to answer the question!
More...

I know exactly what you're talking about.

It's probably less than 1%. But why does it matter?

There is no published distribution curve for stock market returns. It doesn't exist. And the curve isn't binomial or normal. Trading is a zero-sum game. And most traders lose. So, if a distribution curve did exist, it'd be flat for ~98% with an exponential positive tail at the end (>2%).

The only way to guesstimate is run a monte carlo.

Take your average win (take profit), average loss (stop), and total number of trades.

Run the simulator on the exact same data with the tp and stop and see how many iterations it takes to achieve a 7.5% return.

Get it ?

Edit: Major broker/dealers/banks aggregate their clients performance statistics and likely possess the type of distribution curve for returns you want. But that stuff is all internal and proprietary.
 
anesthesiaman,

To get the precise answer to the question you are asking, I would suggest picking up a copy of...
http://www.amazon.com/Evidence-Base...2?ie=UTF8&s=books&qid=1286259746&sr=8-2-spell
... for some common approaches to solve your p-value based question as applied to trading.

As one poster suggested earlier, you could run several hundred iterations of monte carlo simulations for terminal wealth gain with random entry and exit over the instrument and period you traded, find the rightmost tail area of the distribution which corresponds to 1% or 5% of the total area, and see if your results lie inside the 99 or 95% region or outside to reject the null hypothesis of returns due to chance. If you generated thirty trades, then you can generate a sampling distribution with averages of each set of simulated trades to generate the underlying sampling distribution, and compare your average performance, etc. There are also t-test approaches, but that's the general statistical based answer.

Incidentally, your average returns for the chance based analysis need not be equal to zero; rather it would be equal to the bias of the instrument during the period over which you traded.
 
Quote from dtrader98:


As one poster suggested earlier, you could run several hundred iterations of monte carlo simulations for terminal wealth with random entry and exit, find the rightmost tail area of the distribution which corresponds to 1% or 5% of the total area, and see if your results lie inside the 99 or 95% region or outside to reject the null hypothesis of returns due to chance. .
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That's a better idea. I figured use the average tp and loss and run it several times and see how many iterations it takes for each cycle to hit the target. Take the average of the set = ~probability. But yes, random entry/exit is better and see where the target lies in relation to the 1 and 5% barriers. Stats. meh.
 
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