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RFMontraz
NP Italian Stallion

Total Posts: 2019
Joined: Mar 2004
 
Posted: 2006-01-10 16:31

As described in Fortune's Formula (I hope to remember correctly as I don't have the book in front of me) Shannon came up with this idea.

Pick a stock that doubles or halves everyday (50% chance of that happening) and put 50% of your funds in it leaving the other 50% in cash. Rebalance everyday. You end up making a lot of money off a random walk.

Does it actually work? Shannon says no because the commissions would kill you. But the crucial problem (as noted by the author) seems to find a stock that volatile (without the risk of going bankrupt for good, i.e. game over).

Can you think of anything that  behaves that way? Commodities? Currencies? Art? Stamps? Pink sheet stocks (they do go bust but you can modify the system and diversify if the odds work)? Furs? Umbrellas? (I'm actually serious, I'm trying to think of something seasonal/cyclical/fashionable - well you get the idea)

 


I've got 99 problems but a bitch ain't one

ballsup


Total Posts: 90
Joined: Dec 2004
 
Posted: 2006-01-10 16:44
I think the closest you'de get to this is going down the bookie. But instead of keeping half your ante they'll take it all. I wander why that is??

NIP247


Total Posts: 544
Joined: Feb 2005
 
Posted: 2006-01-10 17:12

Shannons idea was later popularized by Thomas Cover, spreading the concept of "universal portfolios" ( also goes by the name of "volatility pumping"), which given a certain number of criteria would beat the best stock in the selection universe in hindsight.

Claude Shannon, Thomas Cover, dig deeper and Mr Simons will show up as well ( or his predecessor...)

Thomas Cover's book Elements of Information Theory has a chapter on information theory and the stock market.

Further interesting articles are found here

Issues are how to 1)optimize the rebalancing process 2) take account of transaction costs (discussed by Bloom and Kalai) 3)be able to both go long and short ( discussed by Cross & Barron)

This french gentleman claims to have implemented such algorithms. I would be very interested in taking a deeper look into them, for sure...

 


On your straddle, done on the puts, working the calls...

chiral3
Founding Member

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Posted: 2006-01-10 17:37
would you not need an infinite amount of capital to invest to account for every scenario with no time constraint?

Nonius is Satoshi Nakamoto. 物の哀れ

Nonius
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Nonius Unbound
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Posted: 2006-01-10 23:32

shit, does this mean RFM is gonna start talkin about Kelly?

anyway, if you start with 1 dollar, then, after n days your wealth goes to:

1*(1+.5*x1)*(1+.5*x2)*.....*(1+.5*xn) where xi denotes the random variable of the ith day's return.

if the returns are independent, then the expected wealth after n days is the product of the expectations.  but computing one of those expectations yields:

0.5*(1+.5)+.5*(1-.5*.5)=1.25.

so, your expected wealth after n days is (1.25)^n

for me the big issue is simply the stylized assumption that returns are stationary.

nothing behaves like this stock, other than my blood pressure.


Chiral is Tyler Durden

TonyC
Nuclear Energy Trader

Total Posts: 1284
Joined: May 2004
 
Posted: 2006-01-11 00:17
>nothing behaves like this stock, other than my blood pressure.

Ah, but could one construct an option portfolio that behaved like [a less volatile] version of this stock, and then trade in and out of that option portfolio . . .

more generally

Cover showed that for the universal portfolio to beat the "best stock in the market" the universe of stocks had to have AT LEAST ONE stock that was sufficiently volatile and whose correlation coef. was sufficiently below "1"

the more stocks that met the criterion, the more volatile that set of stocks, the greater the distance from correlation coef. of "1", the quicker the universal algorithm would beat the best stock . . .

so could one construct a portfolio of options across, say, 5 asset classes, whose volatility and correlation coef. were, BY CONSTRUCTION, sufficient to beat the best asset in, say, 2 years, and trade in and out of those portfolio[s]?



flaneur/boulevardier/remittance man/energy trader

Nonius
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Posted: 2006-01-11 07:20

Ah, but could one construct an option portfolio that behaved like [a less volatile] version of this stock, and then trade in and out of that option portfolio . . .

Well, but that option portfolio would have a characteristic that the stock wouldn't have- theta. 


Chiral is Tyler Durden

Graeme


Total Posts: 1629
Joined: Jun 2004
 
Posted: 2006-01-11 09:27

I haven't thought this through (well, at all), but this seems very similar to the gambler's suicide stategy viz. bet on red (in roulette), if you win, you've doubled up, go home, if you lose, double your bet. Iterate.

In this strategy you are guaranteed to double up EXCEPT you might run out of cash/credit. In other words, you aren't.

To exclude these strategies is important in much martingale theory where it needs to be specified that the process is bounded below (which this gambler's suicide strategy isn't).

To make my post completely explicit, it would be interesting to hear opinions on the similarities/differences between these two strategies.


Graeme West

NIP247


Total Posts: 544
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Posted: 2006-01-11 09:46

gambler's suicide stategy viz. bet on red (in roulette), if you win, you've doubled up, go home, if you lose, double your bet. Iterate

In the universal portfolio case, you don't go home when you win, and you don't double up when you lose as you always invest a fraction of your assets in every instrument.

Otherwise, the main difference with roulette is the diversity of your investment universe, the lower transaction costs (slippage < house edge), the lower ticksize of bets ( you run out of cash only at the limit ) and the fact that you can stay a little longer at the table with a winning strategy without risking meeting this gentleman with a hammer ready to smash your fingers into "fleshy bone meal"

 


On your straddle, done on the puts, working the calls...

RFMontraz
NP Italian Stallion

Total Posts: 2019
Joined: Mar 2004
 
Posted: 2006-01-11 10:16

would you not need an infinite amount of capital to invest to account for every scenario with no time constraint?

No you don't, my initial post probably wasn't very clear. Say you start with $100, you put $50 in the stock. The stock loses 50%, you rebalance the capital you are left with ($75) in order to have $37.5 invested in that stock (so you have bought more) and $37.5 in cash and so on. As you can see you get to lose it all only if the price creeps to 0 (and stays there). Until then you can play as long as you want. Hence the idea is to avoid any asset that potentially can plummet to zero (hence I'd say no to a single stock or a single option).

The problem with options is (as Dr N. already said) that you have to pay theta which, given the long biased strategy, works against you.

Honestly even if you do buy more when it's going agaist you I don't see any similarity with the gambler suicide. You can lose as many times as you want (not considering commissions here for the sake of the argument) and you'll never run out of credit/cash. The problem is that you assume (as Dr N. said) a positive expectation from the "game" (+100%/-50%)

Given that Nonius blood pressure is:

  1. not tradable
  2. will go to zero and stay there

can you guys think of anything that fits the picture?

{Edit: Xposted with NIP}


I've got 99 problems but a bitch ain't one

shavinOccam


Total Posts: 210
Joined: Oct 2005
 
Posted: 2006-01-11 14:01
volatility is an autocorrelated phenomenon. rank the sp1500 universe by range traded during last five days. take the 100 top rangers. from these take those who went up most or went down least. thus trying to shift expectations a little away from the zero-expectation zone. build an index out these fifty, calc its range and see how much leverage you need to get to your 50%. well, actually you'd need too much leverage probably, but you could extend the trading length until it fits. five days should do fine. basket trade and woops

RFMontraz
NP Italian Stallion

Total Posts: 2019
Joined: Mar 2004
 
Posted: 2006-01-11 14:13
If you use leverage you can go bust (better "blow up", losing more than your initial capital). Don't think leverage is allowed to exploit this "idea".

I've got 99 problems but a bitch ain't one

NIP247


Total Posts: 544
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Posted: 2006-01-11 14:26

shavinOccam, I think the Universal Portfolio algorithms have a dominantly contrarian weighting scheme. The weights will "learn" to hold a little more of the outperforming stocks but it takes a very long time and every step before that, any outperforming stock will be pumped out of money used to redistribute in other less well performing assets. That's according to my understanding.

 


On your straddle, done on the puts, working the calls...

kr
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Posted: 2006-01-11 22:41
I still don't quite get it - yes, you will never actually get stopped out BUT you may reach such a low level that it will take forever to return to your starting position, no?  And I'm still a bit doubtful that it works correctly, because the stock drift is still mu - sigma^2 / 2, and with big vols the second term is going to dominate. 

Actually this strategy is now unlike CPPI in retail products.  The problem there is really the opposite problem compared to Petersburg - that is, if you keep winning, pretty soon your position is going to be too large compared to the float and the process will defeat itself.  In CPPI the risky asset is a hedge fund strategy that really ought to have a fairly low ceiling - i.e. how much exposure you can possibly have. 

I do wonder if this kind of strategy is interesting because it forces us off the part of our utility curve that we know well.  If you lose half the value and are still comfortable saying, "Screw it, we rebalance and go for it again", you are really in a purely rational world (maybe even more so if you are still doubling down after several wins).  Maybe the essential thing here is that you try to force yourself away from everybody else's utility curve - sort of like 'behavioral arb' if you'll tolerate my bastardization.  I might even point to Taleb saying "you never get comfortable paying your option premia every day in the hopes of an unlikely event". 

my bank got pwnd

NIP247


Total Posts: 544
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Posted: 2006-01-11 23:14

...you may reach such a low level that it will take forever to return to your starting position, no?

Worse case scenario, yes, but doesn't really happen in practice. The drawdowns are nonetheless horrific-

The problem there is really the opposite problem compared to Petersburg - that is, if you keep winning, pretty soon your position is going to be too large compared to the float and the process will defeat itself

Also true in playback with no consideration to slippage and trans costs. In practice though, you need to find an optimal rebalancing rule so that you don't keep churning your portfolio. You lose the optimality in being able to rebalance in the hypothetical near-continuous time and thereby also the compounding effect. The results on final P/L are dramatically lowered so your position never gets that big Smiley

The first Thomas Cover papers spurred a whole lot of research in the area, all of them using the same dataset of NYSE stocks, for the purpose of benchmarking. Results of the original Cover algorithm and extensions of his models are available in Borodin and Blum and Kalai.

What I especially like about Borodin is that he plays the strategy backwards in time and still produces ok results. So all is not an effect of the huge bullmarket. Nevertheless there is survivorship bias in the results...

 


On your straddle, done on the puts, working the calls...

Nonius
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Posted: 2006-01-12 05:24

sure the bid-ask spread is a 'nonlinear' component addition to the log utility optimization scheme. churning is ok as long as you add a constraint when calculating your fortune formula bet size.  this constraint is that it is that the expected return is above a bid-ask (or more generally a cost) hurdle. 

as for continuous limit, this is just a stylized trick to apply CLT.  the upshot is that you don't give a shit, in the continuous limit, about skew, kurtosis, corrrelation manifold dynamics, and the number of angels on the head of a pin, you care about mean and standard deviation.


Chiral is Tyler Durden

jaiman


Total Posts: 250
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Posted: 2006-01-13 00:08

sorry, i mis-read the original post. Blush


Nonius
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Posted: 2006-01-17 22:32

well, since Adennenberg, the Kelly King, is logged on...I thought I'd post this little excel exercise....take a stock with a 5% growth rate and 15% vol.  scale first to daily trades, then to intraday trades using Kelly.  synthetically create the returns.  after a spreadsheet row's worth of returns, you be in the money or not?  basically, 5%/15% assumption implies a 2.22 leverage ratio.

edit: I mean't a spreadsheet column's worth of returns.....


Chiral is Tyler Durden

Nonius
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Posted: 2006-02-08 10:38

Claude Shannon, Thomas Cover, dig deeper and Mr Simons will show up as well ( or his predecessor...)

It's interesting that Berlekamp took out the passage about selling out his interests to precisely Simons. 


Chiral is Tyler Durden

NIP247


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Posted: 2006-02-08 23:50

Indeed!

 


On your straddle, done on the puts, working the calls...

Nonius
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Nonius Unbound
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Posted: 2006-02-08 23:52
to me, it confirms that half of Simons deal is modified kelly....dunno, seems like it to me.

Chiral is Tyler Durden

NIP247


Total Posts: 544
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Posted: 2006-02-08 23:55

Agreed, that's why I was keen on knowing what that french chap at www.yats.com was doing. Anyway, the thing about buying out external investors is slightly reminiscent of another hugely successful fund...

"c'est l'histoire d'un homme qui tombe du 5eme etage [...] jusqu'ici tout va bien..."

 

 


On your straddle, done on the puts, working the calls...

akimon


Total Posts: 566
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Posted: 2006-02-09 00:56
is shannon the same guy who started using the concept of "entropy" to quantify uncertainty in probability and information theory?

Patrik
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Posted: 2006-02-09 01:05
yep, this guy

Capital Structure Demolition LLC Radiation

akimon


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Posted: 2006-02-09 01:25
cool... i never knew he had anything to do with finance or investments!

his theories came up all the time in my old telecommunications and signals engineering classes.
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