SKILL or LUCK???

[SplawnDarts]

You can answer your own question using the cumulative binomial distribution in Excel or similar eg. =BINOMDIST(85,132,0.5,TRUE)

Note that the number of heads is reduced by 1, since you're summing up the probability of a worse performance and should stop there, not at 86.

99.97% of results, if generated by chance, would be worse. So if this was pulled from a population of one actual historical result (rather than, say, backtesting millions of strategies) then it's almost certainly skill rather than luck.

And of course the usual ET mathematical illiterates are out in force in this thread.

 

[panzerman]

A coin toss is exactly a random process. Its outcomes create a binomial distribution given a sufficiently large number of trails, and has no skew or kurtosis. Stock prices (or returns rather) also have a normal distribution, but that distribution includes some amount of skew and kurtosis.

In other words, stock price is too random for technical analysis to work consistently, yet not random enough to account for all the possible risks. For example tail risk when selling naked OTM options.

 

[Scataphagos]

"... stock price is too random for technical analysis to work consistently...

False conclusion. Way, WAY, WAAAYYYY F'ING FALSE!

Suggest.... Don't bother posting further on this topic... nobody with half-a-brain would consider anything else you have to say.

(Your response to this post will likely get you onto my IGNORE list... but please go ahead and give me a chance to change my mind.)

 

[Scataphagos]

As a rational type of person, a mathematician, and a scholar, do you believe that the above applies to all types of trading?

What are "types of trading"??

 

[George Canuck]

You can answer your own question using the cumulative binomial distribution in Excel or similar eg. =BINOMDIST(85,132,0.5,TRUE)

Note that the number of heads is reduced by 1, since you're summing up the probability of a worse performance and should stop there, not at 86.

99.97% of results, if generated by chance, would be worse. So if this was pulled from a population of one actual historical result (rather than, say, backtesting millions of strategies) then it's almost certainly skill rather than luck.

And of course the usual ET mathematical illiterates are out in force in this thread.

SplawnDarts, thank you for a definite answer! Indeed, I am absolutely stunned by your figure (99.97%) since I was expecting something closer to 80% or so. (Incidentally, this is actual real-life performance, not paper trading or computer simulation.)

May I ask you the following?

Are the results of 132 trades statistically significant? Or do I need the results of (say) 500 or 1,000 trades to do a proper performance evaluation?

Also, does this figure (99.97%) need to be adjusted, presumably downward, given my average loss is slightly more than my average win? Or is average win/loss value not relevant to the calculation itself?

 

[panzerman]

I'm glad Georgy boy made money, but N=132 is still a rather small population set. Yes it is possible to make money from a random walk process, but if he backtested his method, I bet you would see results closer to breakeven.

Scataphagos, why not post your TA method(s) you have used for the past 3 years and a P/L statement to match? Positive expectancy is all I'd want to see, not necessarily a high win percent. An anonymous forum sure is good when you want to be a tough guy isn't it?

 

[SplawnDarts]

SplawnDarts, thank you for a definite answer! Indeed, I am absolutely stunned by your figure (99.97%) since I was expecting something closer to 80% or so. (Incidentally, this is actual real-life performance, not paper trading or computer simulation.)

May I ask you the following?

Are the results of 132 trades statistically significant? Or do I need the results of (say) 500 or 1,000 trades to do a proper performance evaluation?

Also, does this figure (99.97%) need to be adjusted, presumably downward, given my average loss is slightly more than my average win? Or is average win/loss value not relevant to the calculation itself?

Glad I could be of help.

If you want confidence on a method with non-symmetrical wins and losses, replace the binomial probability of 0.5 with whatever would be required to break even - (AVG_LOSS)/(AVG_WIN+AVG_LOSS). So if you won 1 unit and lost 2, you would put in 0.666.

The number you get out of the binomial distribution math is the statistical confidence - so if it starts with a bunch of 9s, then yes you sample is significant. But you need to recompute with the individual trial probability adjusted for win/loss size - that could tilt the outcome dramatically.

You should also be aware that the market is not always stochastic on the long term. You can have a method that is statistically great, and something underlying changes and it stops working.

 

[SplawnDarts]

One other heads up - if your trading style has situations where large losses or wins can occur - much larger than the win/loss averages - then you need your sample to be big enough to include several examples of those. In contrast if your losses are bounded by relatively tight stops+slippage, and numerous such events occur in the sample then you should be able to draw meaningful conclusions. But methods that don't have solid stops (ie. that have real night/weekend/lack of liquidity risk) are much harder to evaluate. In many cases they can only be proven profitable by putting in an loss limit via purchasing deep OTM options.

 

[aqtrader]

Requesting the help of those mathematically inclined...

Assuming a fair coin, what is the probability of getting 86 heads (non-consecutive) from 132 coin tosses?

I don't know the answer though I do know its not a matter of simple division. One would expect a fair coin to return 66 heads and 66 tails. In the extreme, a fair coin COULD return 132 heads and 0 tails... but presumably such odds would be astronomical.

I ask because I want to compare my two year trading performance (86 wins, 46 losses... avg. win $ 3,800 and avg. loss $ 4,200) against results that could be achieved just by pure chance or luck.

Your help and/or insights would be most appreciated. Thanks!

mathematically, your original question was not actually you wanted after read your more post in the threads. the question should be Assuming a fair coin, what is the probability of getting at least 86 heads (non-consecutive) from 132 coin tosses? because the probability for your original question is extremely small. the probability for the revised version will be reasonable but none in this thread gave you the right answer yet.

 

[SIUYA]

I ask because I want to compare my two year trading performance (86 wins, 46 losses... avg. win $ 3,800 and avg. loss $ 4,200) against results that could be achieved just by pure chance or luck.

Your help and/or insights would be most appreciated. Thanks!

FWIW - you should also compare it to the results of simply investing in the instrument you are trading. Unless you take a long enough sample of trades and time sometimes the comparisons might show its not worth your time and or effort if you are still not doing better than simply investing in it.
Basically you should also be comparing the results that could be achieved by luck of simply investing and doing nothing more.