Arcsinus law: distinguishing trend from persistency of chance

[harrytrader]

This is of course both applicable to humans and trading systems that are based on stochastic trend following as I said here:

http://www.elitetrader.com/vb/showthread.php?s=&postid=394653#post394653

"There is a statistical study of 50 pages made on cocoa futures markets depending if it is LIFFE or CSCE market during 15 years testing about 3000 trading systems from moving average to breakout systems more than 60% were profitable on LIFFE whereas only 12% were profitable on CSCE although it is the same product cocoa. So it is false to say that there is always 95% of losers since purely mechanical systems can majoritely be winners or losers this depends on markets chosen and markets contexts. Once again this is not astonishing if one understands persistency law."

This doesn't mean that these systems are worthless, it means that if there is no trend in the market or period chosen well bad luck there will be loss and not profit. But if there is some trend the use of (some) TAs (because not all TAs are worth) can then help to capture this trend. But it is conditional. It's like the use of strategies in casino: they are useful and better than use of no strategy at all but it won't change the negative expectancy to positive expectancy as I have sometimes read, it will only put all the chances on your side . So diversification is often needed with these systems. This is for TA based on stochastics only which have poor predictive power, for TA based on true market's action it can be better than just put the chance on your side it can really turn the negative expectancy to positive expectancy if it is based on true laws of market and not only on pure stochastics which is sumitted to random law. In that second case diversification is not always needed and even detrimental to performance (I can't speak in general it depends on the system/model. It is the case of my model: it works best with great indices like dow or cac40 not because of better trends than other markets but because of precision of the model so I have no interest to diversify).

Quote from harrytrader:

It's rather that at long term there are only a few percentage of "good traders" but on short term (this is relative of course to period and style of trading this means dozens of years for portfolio managers for example to a few months/years for short term traders) there can be even a majority of winners ... and after that a majority of loosers: that's what persistency means, it's easy to see it during bull phase where all the public and traders believe into a "new era" because it seems to last long time enough (remember arcsinus law is about time not about the distribution of mean which is another law - the central limit theorem) and that everybody seems to be winner . Since at each cycle there are newcomers the same illusion can begin again and again, this on multiple scales.

 

[valleyvintner]

I don't think Brandon has missed anything. Random events like coin tossing inevitably produce a standard distribution (bell curve) UNLESS they're non-random and therefore exhibiting trend behavior. In that case they produce a skewed distribution. The extent and persistence of skew are the basis of the Random Walk Index. Cynthia Kase, who was an engineer before she became queen of technical analysts, derives an impressive set of momentum indicators from this very fact. Her book "Trading With The Odds" gives chapter and verse.

 

[abogdan]

Quote from harrytrader:

This is of course both applicable to humans and trading systems

Could not resist, have to jump in. Skewed distribution curves is a norm. Perfect Gauss distribution is a very rare occasion. This explains why there is an intraday volatility. For example, average intraday volatility of stocks like KLAC, AMAT, QLGC etc. is around 2.2%. I have done some analisys: If you take daily price moves and for each day you take either (High - Open) or (Open -Low) which ever is greater then divide it by Open you would get daily guaranteed price move (Up or Down). For KLAC, for example, there were no days in the past 400 trading days when this move (up or down) was less than 1.045% (Let' say 1%). So, draw a horizontal line each day that starts from Open price. If Bid is higher than this line go LONG 1000 shares. If it goes to 1% right away quit till the next day. If it did not go there and Ask became lower than your horizontal line then flip your position to go SHORT but this time increase your position by 1/10 of your original position (SHORT 1100 shares). Keep on flipping each time taking new position with the shares equal to 1000*(1.1^n) where "n" is a flip count. If you manage to keep the cost of your flips <= $0.05 per share (let's say $0.01 for your commissions, $0.02 for Bid/Ask spread, and $0.02 for slippage) then your losses each time you flip are only 10% of your profit target of $0.5 per share(1% for KLAC). It ensures you that when the price finally goes to 1% either up or down you will pay for all the flips and you will make 1% return. So, if your intraday leverage is 4:1 on your capital you have 15 flips to get you to 1% (1.1^15 = 4). So you did make 1% on your actual money. Now, if you look at KLAC data for the past year, the average amount of flips that it took to get to 1% (up or down) was 5.7! So your actual leverage that you used on average was 1.7. It makes your capital available for other stocks with the same strategy. Effective return will be equal to appr. 1.97% a day which will give you annualized(compounded) about 100*Original capital. Not bad! And there is no risk! You are always "with the market". If you want to be more sophisticated you can use this strategy on daily/monthly data and wright Calls and Puts to pay for the flips. This way you don't even have to increase you shares and your capital usage is better. So, how is this for a random strategy?

 

[valleyvintner]

Quote from abogdan:

If you take daily price moves and for each day you take either (High - Open) or (Open -Low) which ever is greater then divide it by Open you would get daily guaranteed price move (Up or Down). For KLAC, for example, there were no days in the past 400 trading days when this move (up or down) was less than 1.045% (Let' say 1%). So, draw a horizontal line each day that starts from Open price. If Bid is higher than this line go LONG 1000 shares. If it goes to 1% right away quit till the next day. If it did not go there and Ask became lower than your horizontal line then flip your position to go SHORT but this time increase your position by 1/10 of your original position (SHORT 1100 shares). Keep on flipping each time taking new position with the shares equal to 1000*(1.1^n) where "n" is a flip count. If you manage to keep the cost of your flips <= $0.05 per share (let's say $0.01 for your commissions, $0.02 for Bid/Ask spread, and $0.02 for slippage) then your losses each time you flip are only 10% of your profit target of $0.5 per share(1% for KLAC). It ensures you that when the price finally goes to 1% either up or down you will pay for all the flips and you will make 1% return.

This is nice work! This method exploits trend and volatility with minimal risk. Very nice! Provided of course that you can keep the cost of the flips under control.

 

[harrytrader]

Quote from abogdan:

Could not resist, have to jump in. Skewed distribution curves is a norm. Perfect Gauss distribution is a very rare occasion. This explains why there is an intraday volatility.

I agree since this was the title of one of my thread
"Normal distributions are not the norm."
http://www.elitetrader.com/vb/showthread.php?s=&threadid=25943

Nevertheless it depends on definition of "norm". Normal Law is still the norm if norm means "ideal" reference. So one should rather say "normal law" are not so "widespread" as one could think but it is still a useful reference in industry but even in stock market - ie I won't say that it is totally useless I say that for some approach like trading futures it is not good enough. Skewed distribution in stock market is now widely recognised even by academics since Mandelbrott's seminal work. Rather than saying that it explains volatility since skewness is just a statistical parameter - a mere artefact not a cause by itself - I would rather agree with some academic research saying that operators prefer positive third moment -which translate into dissymetry (mean is first moment, variance is second moment) as a logical consequence for risk aversion.

As for the strategy below, I can't judge in details since I don't follow stocks, but in principle I'm not against it for I said here http://www.elitetrader.com/vb/showthread.php?s=&threadid=24585&perpage=6&pagenumber=3 that stock market is not like Casino so that it can exist strategies that are not purely martingale or supermartingale but submartingale (a positive expectancy).

Quote from abogdan:

I have done some analisys: If you take daily price moves and for each day you take either (High - Open) or (Open -Low) which ever is greater then divide it by Open you would get daily guaranteed price move (Up or Down). For KLAC, for example, there were no days in the past 400 trading days when this move (up or down) was less than 1.045% (Let' say 1%). So, draw a horizontal line each day that starts from Open price. If Bid is higher than this line go LONG 1000 shares. If it goes to 1% right away quit till the next day. If it did not go there and Ask became lower than your horizontal line then flip your position to go SHORT but this time increase your position by 1/10 of your original position (SHORT 1100 shares). Keep on flipping each time taking new position with the shares equal to 1000*(1.1^n) where "n" is a flip count. If you manage to keep the cost of your flips <= $0.05 per share (let's say $0.01 for your commissions, $0.02 for Bid/Ask spread, and $0.02 for slippage) then your losses each time you flip are only 10% of your profit target of $0.5 per share(1% for KLAC). It ensures you that when the price finally goes to 1% either up or down you will pay for all the flips and you will make 1% return. So, if your intraday leverage is 4:1 on your capital you have 15 flips to get you to 1% (1.1^15 = 4). So you did make 1% on your actual money. Now, if you look at KLAC data for the past year, the average amount of flips that it took to get to 1% (up or down) was 5.7! So your actual leverage that you used on average was 1.7. It makes your capital available for other stocks with the same strategy. Effective return will be equal to appr. 1.97% a day which will give you annualized(compounded) about 100*Original capital. Not bad! And there is no risk! You are always "with the market". If you want to be more sophisticated you can use this strategy on daily/monthly data and wright Calls and Puts to pay for the flips. This way you don't even have to increase you shares and your capital usage is better. So, how is this for a random strategy?