# Parrondo's Paradox



## ThingyMajiggy (3 June 2010)

Has anyone ever read up about this concept? 

It is an idea that suggests it is possible to have a winning strategy simply by switching between 2 losing subjects, in all areas of life not just the markets. 

eg. insects and birds destroying a crop, if you have just 1 of them, there is a problem, your crop is going to be destroyed some what, but if there were both, the bird and the insect, there is a high chance the bird would eat the insect and the actual damage to your crop would be less, but each individually would be a negative impact on your crop, but mixing them together and swapping between the 2, the damage is actually less by having 2 "negative" impacting things...or something like that 



> *PLAYING THE MARKET*
> 
> Interestingly, people already exploit switching strategies similar to Parrondo's in everyday life though not, of course, because they are applying theoretical insights about Brownian motion. But whenever someone changes jobs to get a salary increase, for instance, or sells peaking stocks and buys slumping ones, Parrondo's paradox comes into play. Moreover, many ordinary events are governed by random-seeming fluctuations, from the ups and downs of the financial markets to the succession of political parties in power. Economists and mathematicians have begun to ask whether the principles of Parrondo's paradox could apply to decision making in those realms.
> 
> The physicist Sergei Maslov of Brookhaven National Laboratory in New York has shown that principles similar to Parrondo's paradox can be applied to the stock market. Maslov found a way that the value of a stock portfolio can increase even if all of its stocks decline in the long run: The entire portfolio must be sold periodically even daily and the proceeds must be quickly plowed back into repurchasing the stocks in the same proportions as they were in the original portfolio. The net effect of such periodic rebalancing is to apply the gains from stocks that are doing temporarily better than average (and have therefore increased their relative proportion in the portfolio) to buy more stocks that are temporarily underachieving. The beauty of Maslov's proposal is that one need not know anything about particular stocks; simply sell them all and then buy them back in a rebalanced portfolio. Unless the balance of investments is shifted in that way, the long-term prospects for a portfolio full of duds are grim indeed, says Maslov, since all of the stocks tend to decline with time. But Maslov's tactic can generate better returns than the buy and hold policy that is the current favorite of many economists. (It should be noted, however, that the declines in technology stocks mentioned at the beginning of this article might well overcome even Maslov's strategy.)




http://www.eleceng.adelaide.edu.au/Groups/parrondo/intro.html#introduction

http://www.eleceng.adelaide.edu.au/Groups/parrondo/articles/Playing both sides, Erica Klarreich.htm

http://www.eleceng.adelaide.edu.au/Groups/parrondo/articles/nytimes.html

http://pagesperso-orange.fr/jean-paul.davalan/proba/parr/index-en.html

I find this sort of thing very interesting, whether it can be used effectively is another matter, but this is just purely for discussion. It would be interesting to try this theory out, but I'm not sure how that could be done, anyone got any ideas or ever experimented with this sort of thing?

I have only just discovered this and been reading about it, so I don't know if its a common known thing or not, forgive me if it is, but I have never heard of it before.


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## barney (3 June 2010)

Howdy Sam .... It is interesting I agree. I tend to think a mathematical advantage is often a lot more useful than a discretionary trading concept, but unfortunately my attempts at that kind of concept have been pretty average

Nioka on the ADI thread has pretty much got this idea down pat, and perhaps his/her/felix the cat may be able to shed a bit more light on the best way to implement it.
Cheers.


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## ThingyMajiggy (3 June 2010)

barney said:


> Howdy Sam .... It is interesting I agree. I tend to think a mathematical advantage is often a lot more useful than a discretionary trading concept, but unfortunately my attempts at that kind of concept have been pretty average




What makes you think that?



barney said:


> Nioka on the ADI thread has pretty much got this idea down pat, and perhaps his/her/felix the cat may be able to shed a bit more light on the best way to implement it.
> Cheers.




Ok, hopefully he can shed more light on it, if he has been using this method in his real trading


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## barney (4 June 2010)

ThingyMajiggy said:


> What makes you think that?




Just a random example would be trading forex as price tends to fluctuate between high and low range extremes moreso than stocks.  Instead of using standard tech analysis, using derivatives of the weekly/daily/hourly range, and where price is at a point, "x" number of pips either side of the "typical" average value range, it is plausible to scale in and out of positions for profit, based solely on the instruments "usual" characteristics.  Kind of a mean reversion technique. By entering positions after the extension of the mean has been severely violated, mathematically it is more likely the position will reverse. Trouble is theory doesnt alway work in practice  



ThingyMajiggy said:


> Ok, hopefully he can shed more light on it, if he has been using this method in his real trading




Nioka can verify, but he traded an initial small amount of shares between two companies as they both dropped in price. Because the "relative" value was never static, trading the higher value for the lower value share resulted in a huge increase in the number of shares held ....  Of course, the plan will still only work if/when the share price eventually appreciates, but it certainly fits the Parrondo Paradox concept.   
Cheers.


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## brty (4 June 2010)

Sam,



> eg. insects and birds destroying a crop, if you have just 1 of them, there is a problem, your crop is going to be destroyed some what, but if there were both, the bird and the insect, there is a high chance the bird would eat the insect and the actual damage to your crop would be less, but each individually would be a negative impact on your crop, but mixing them together and swapping between the 2, the damage is actually less by having 2 "negative" impacting things...or something like that




I hope it is something like that rather than the above. I know from experience that when birds are destroying a crop they will keep doing it and not choose the insects instead. To keep birds from destroying a high value crop you have to net. By netting you do indeed increase the number of insects, but only because you keep the insect eating birds out, as well as the crop eating ones.

brty



brty


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## ThingyMajiggy (4 June 2010)

brty said:


> Sam,
> 
> 
> 
> ...




Yeah don't put too much weight on that paragraph of mine, I was trying to remember it as best I could from reading it earlier, but obviously didn't get it right, couldn't find where I had read it from again  It would be interesting to see if they would though, if you kept the birds out by netting, therefore increasing the insects and causing potentially more damage to the crop anyway, I wonder if that, compared to having birds and insects in there together would be more or less damage than netting, based purely on the paradox idea, we could get into sprays etc to keep the bugs out but lets not bother getting quite that technical 

Still an interesting idea, even if I did **** up the description


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## Wysiwyg (4 June 2010)

barney said:


> Just a random example would be trading forex as price tends to fluctuate between high and low range extremes moreso than stocks.  Instead of using standard tech analysis, using derivatives of the weekly/daily/hourly range, and where price is at a point, "x" number of pips either side of the "typical" average value range, it is plausible to scale in and out of positions for profit, based solely on the instruments "usual" characteristics.  Kind of a mean reversion technique. By entering positions after the extension of the mean has been severely violated, mathematically it is more likely the position will reverse. Trouble is theory doesnt alway work in practice
> Cheers.




Additionally, correlation between an independent security and it's dependent can be quantified by observing a correlation strength between the two securities. Like stock B  moves X amount to stock A's move, averaged out over a given sample of data. Within the ASX there are stocks that are highly correlated to an index while others are lowly correlated. The rest are in between and can be measured on a scale from high to low. 
So an algorithm can be written to list stocks from the  highly correlated to the lowly correlated over a given sample of data. I'm sure there are complex algorithms that squeeze every statistic out of a given sample of data to find the "most likely" scenario to unfold.


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## Wysiwyg (4 June 2010)

ThingyMajiggy said:


> H
> eg. insects and birds destroying a crop, if you have just 1 of them, there is a problem, your crop is going to be destroyed some what, but if there were both, the bird and the insect, there is a high chance the bird would eat the insect and the actual damage to your crop would be less, but each individually would be a negative impact on your crop, but mixing them together and swapping between the 2, the damage is actually less by having 2 "negative" impacting things...or something like that




Humans tried similar with the introduction of the Cane Toad into sugar cane fields to eat the Cane Beetle. Who would have thought the first few releases would eventually grow to over 200 million.  Not the Bureau of the time. 



> Cane toads were introduced to Australia from Hawaii in June 1935 by the Bureau of Sugar Experiment Stations in an attempt to control the native Cane Beetle (Dermolepida albohirtum). They bred immediately in captivity, and by August 1935 more than 102 young toads were released in areas around Cairns, Gordonvale and Innisfail in northern Queensland. More toads were released around Ingham, Ayr, Mackay and Bundaberg. *Releases were temporarily limited because of environmental* *concerns but resumed in other areas after September 1936*. Since their release, toads have rapidly multiplied in population and now number over 200 million and have been known to spread diseases affecting local biodiversity.


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## barney (6 June 2010)

Wysiwyg said:


> Additionally, correlation between an independent security and it's dependent can be quantified by observing a correlation strength between the two securities. Like stock B  moves X amount to stock A's move, averaged out over a given sample of data. Within the ASX there are stocks that are highly correlated to an index while others are lowly correlated. The rest are in between and can be measured on a scale from high to low.
> So an algorithm can be written to list stocks from the  highly correlated to the lowly correlated over a given sample of data. I'm sure there are complex algorithms that squeeze every statistic out of a given sample of data to find the "most likely" scenario to unfold.




Howdy Wys .....  Its an interesting concept with a multiple of potential scenarios from a mathematical point of view. Have you traded any of these ideas?

Just an observation with regard to correlated FX pairs which is a bit Parrondo orientated ....

There have been quite a few recent opportunities where the USD/CHF and the EUR/USD, which are generally *oppositely* correlated, have gotten out of sync, and a position taken simultaneously in the *same* direction would have resulted in better than modest gains. 

I'm sure professional FX traders would be using these situations as a potential "leading" indicator to back up their analysis..... I'm not sure they would be taking same direction trades on opposite performing FX pairs, but then again, maybe it is possible, if it lowers risk.  Food for thought. 
Cheers.


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## Wysiwyg (6 June 2010)

barney said:


> Howdy Wys .....  Its an interesting concept with a multiple of potential scenarios from a mathematical point of view. Have you traded any of these ideas?



No Barney. I am aware of this and as yet can't create a list of highly to lowly correlated. Only by looking at two charts at present. A coding expert might be able to create something based on a price rate of change equivalent.


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## howardbandy (7 June 2010)

Greetings all --

I looked at this a couple of years ago.  It seemed to me that to be practical for trading, it was necessary to have good models for both series and at least one of the series had to have a positive expectancy.  By the time I had the metasystem using Parrondo working, there was enough information in the algorithms I had developed that I did not need Parrondo any more.

But there are probably other techniques.

Thanks,
Howard


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