Forums  > Trading  > Shannon's Demon  
     
Page 2 of 4Goto to page: 1, [2], 3, 4 Prev Next
Display using:  

lexx


Total Posts: 60
Joined: Apr 2006
 
Posted: 2006-04-21 17:24
Is there a separate thread on Universal Portfolios ?
Interesting to hear about other peoples' experience with
the concept.

Another paper on them :
www.math.ku.dk/~dlando/bhl.ps
On Long Run Portfolio Optimization Using
Universal Portfolios
Martin Blaedel, Brian Huge and David Lando

Seems concept doesn't work well when assets are correlated.
Another interesting version of the concept :
L. Györfi, G. Lugosi, and F. Udina (2006), "Nonparametric kernel-based sequential investment strategies.''
(available on lugosi's web-site: http://www.econ.upf.es/~lugosi/pubs.html)

Tried it on DJ index stocks.
After 2000 portfolio couldn't achieve any significant result,
also high turnover and as a consequence- transaction costs.

Have a suspicion, that often results which are presented in such papers, are tied up to the data set used, and are not easily achievable in other cases.


LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-22 15:49

Is there a separate thread on Universal Portfolios?

Why don't you start one? I like the idea, but I don't think it works. I think the problem is that it ideally works if applied to the entire market, and if it's continuously rebalanced. Each of these requirements is just as bad as the Black Scholes continuous hedging requirement.

What will happen next is that people will have to start developing discrete versions and approximations, but that's a subject on its own.

What I still don't understand is why shorting is not allowed. If shorting is not allowed, then how would the startegy work in bear markets?


Time is on my side.

opmtrader
Founding Member

Total Posts: 1333
Joined: Mar 2004
 
Posted: 2006-04-23 05:45

I just got done doing a Monte Carlo script for this strategy, however when all the results were converging to zero, I came back and reread the thread.

As RFM said, you need to find a security that either goes up +100% or down only -50%.  I was doing 100%/-100% (double your bet or lose the entire bet) which was wrong.  In that case I agree that finding such a security would be incredibly difficult.

TonyC, in terms of the options portfolio, what kind of position typically moves like that (+100%/-50%).  I say "typically" because I think a big part of this approach is to be devoid of any special selection skills. 

 


FDAXHunter
Founding Member

Total Posts: 8362
Joined: Mar 2004
 
Posted: 2006-04-23 08:14

opmtrader: TonyC, in terms of the options portfolio, what kind of position typically moves like that (+100%/-50%).


Short term vertical spreads (i.e. bear/bull spreads) or binary options. If you have 1 dollar and invest buy 1.5 binaries struck so that it's price equals 1.5/0.5 = 0.333, you have a portfolio that will either be worth either

  • 0.5 (binaries expire worthless, you paid 0.3333·1.5 = 0.5 for them). Return = -50%.
  • 2 (binaries expire in the money, so you have 1.5+0.5= 2). Return = 100%.

Note that you will see the -50% case twice as often as the +100%.

An easier way (with some assumptions) is just to buy an instrument with tick size, say 1 and a price of say 50 and trade a synthetic gamma of 1.
I.e. in a 2 period binomial tree we have:

T=1

T=2

T=3

 

 

52
(value = 3)

 

51
(buy another 1)

 

50
(buy 1)

 

50
(value = -1)

 

49
(sell 1)

 

 

 

48
(value = -1)

Obviously a tree like that violates the log-normality assumption, but never mind that. This is unimportant if we make Δt small enough.
So, if you invest 1 dollar in this strategy, you end up with the same payoff as the binary option (actually, you'd invest 0.5 dollars in it and only trade 0.5 gamma, in which case you either make 1.5 bucks or lose your 0.5).
Put that strategy together in a portfolio with another 0.5 dollars in cash and you end up at period two with either 0.5 dollars or 2 dollars. Which again represents -50% or 100%

Regards.


The Figs Protocol.

LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-23 13:53

Note that you will see the -50% case twice as often as the +100%.

My understanding of Cover's work is that (in the simplest possible example that he uses for illustration) he wants a stock that goes up +100% or down %50 with equal frequency, for example, alternately.

In the market that he discusses as a very basic example, there are two stocks: One has constant value. The other behaves as above. If you invest in only one of them, you will at most double your money (that's when you invest in the volatile one, and it doubles in value rather than halves after the first period). A portfolio of both, that's continuously rebalanced, grows geometrically.

It's a very pretty observation.


Time is on my side.

kr
Founding Member
NP Raider
Total Posts: 3561
Joined: Apr 2004
 
Posted: 2006-04-23 16:47
I still think FDAX's approach is the right one - in order to find something with such massive volatility and skew, some kind of option is probably the best place to look. 

Really, I don't see why a site full of quantitative people haven't blown this apart already - ok, maybe there are some reputable names behind the theory, but it looks crap from both a quantitative AND qualitative point of view.  Quantitative b/c something that either doubles or halves each period naturally has a big positive drift, which would look like a free lunch unless it wasn't.  And it wouldn't be a free lunch if it were an asset with massive skew.  Existing theories don't really deal much with skew - seems that Markowitz was enough to keep people busy up until the present.  Anyhow, if you happened to pick an asset with more normal properties, and not a golden-egg-laying goose, all that doubling-down means that when the bad part of the skew kicks in, you'll be right back where you started in a flash.  To me, it looks as if the experiment is rigged to maximize survivorship bias.

Qualitatively, it seems nobody can find such a golden-egg-laying goose, or even one with that much volatility.  Even the pink sheets typically don't have this kind of volatility in the normal sense - they just have a lot of outliers. 

BTW, the discussion of theta as regards the option in this context is not really correct.  What has been said is what one would do if one were in the risk-neutral hedging position.  However, if the stock tends to drift upwards, then so would the option.  That is just monotonicity of the payoff.  So if you bought options on a stock whose actual process was
dS / S = 12.5% dt + 1600% dW_t, you would expect to see an even stronger positive drift.  At least, up until the point when the stock decided to give back all its gains and demonstrate its 'true' incremental distribution, with an ugly downside tail. 

Anyhow, this just demonstrates that an academic approach can be worse than useless - I think the whole thing is quite misleading.  I've reread the whole thread now, and the only reason I can come up with that might have any legitimate basis at all is that such a high volatility (or even high-skew) situation would put traders well out of their comfort zone all the time, leading to a behavioral result which might be quite distinct from low-volatility trades.  In particular, if traders tend to let their losses run and lock in their gains, then the rebalancing strategy would be contrarian in a behavioral way.  To validate this kind of theory requires a lot more data though.  In particular, (a) it won't work for currencies and (b) it requires an asset with massive volatility, which we still haven't found.  Wake me up when we find one. 

my bank got pwnd

FDAXHunter
Founding Member

Total Posts: 8362
Joined: Mar 2004
 
Posted: 2006-04-23 17:15
LongTheta: he wants a stock that goes up +100% or down %50 with equal frequency

Yeah we all want a bet where we can win 1 dollar and lose 50 cents with a 50/50 probability. Because that's what that wish boils down to. Let me know if you find one Wink

Real pretty observation that.

The Figs Protocol.

opmtrader
Founding Member

Total Posts: 1333
Joined: Mar 2004
 
Posted: 2006-04-23 18:49

Yeah not to pile on here, but it seems more like Shannon's Dreamin' not Shannon's Demon.  You're starting with a massively possitive expectation.

I guess you could apply this if you had found a system with the requisite 2:1 payoff with 50% odds.  The big problem however, as everyone has pointed out, is how do you know that the distribution doesn't change in the future for that setup?  That's the key question in all systems trading I guess.

In terms of binary options, that was my thought last night, but again this was before the 2:1 payoff at 50% odds realization.  I found InTrade.com trading in them.  Has anyone traded there?  What are the spreads like?  Seems like if you had a system that predicted the daily direction of the market at > 50%, but your maginitude of win/loss in the underlying was not profitable, you could make the system profitable using a binary option.  Kinda cool thought.  Anyone doing that?

 

 


LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-23 22:52

Yeah we all want a bet where we can win 1 dollar and lose 50 cents with a 50/50 probability.

He wants a stock that goes up and down, up and down, forever. Never asymptotes to 0 and stays there. If you have that, you pump money from that to a cash account. That's what he calls "volatility pimping". We've all seen such ideas before. Isn't that what they call "scale trading"?


Time is on my side.

Johnny
Founding Member

Total Posts: 4333
Joined: May 2004
 
Posted: 2006-04-24 10:01

I haven't read the article, but this looks like a variation on the familiar BSM replicating portfolio argument.

The replicating portfolio argument says that (in a world of zero transaction costs etc) we can replicate the payoff of the {+100% / -50%} asset by appling a dynamic trading strategy to a portfolio of a risky asset following a gbm process and a riskless asset paying the rf rate. Playing this in reverse suggests that, given a {+100% / -50%} asset and a riskless asset we can follow a dynamic trading strategy to replicate a portfolio that follows a gbm process, i.e. which grows geometrically.

So then we are left with (at least) two practical difficulties. First, where does this {+100% / -50%} asset come from in the first place? And second, the usual difficulty with continuous re-hedging. But practical difficulties aside, this looks to me like BSM in reverse. Would anyone that has read the article care to comment?


Stab Art Radiation CSD LLC

LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-24 12:14

Johnny,

It's a lot simpler than that. His constant stock is a cash account. His volatile stock goes up and down, up and down, forever and ever, in a basically predictable way: You know it will never go too low and stay too low. What's he's doing by "balancing the portfolio" is to buy the stock when it's low and sell it when it's high, forever and ever Big Smile

On the other hand, he's not a stupid man, and he never says that that's a realistic model. To him, that's an oversimplified model, just to give you the idea of his idea.

His idea is that there is a stock market and fund managers will always work with some portflio of stocks from that market. Assuming that the entire stock market doesn't go down and stay down, and assuming that at least part of the market will stay alive, he proves that his universal portfolio will beat any other fixed portfolio in the long run.

Tranaction costs aside, you know what happens in the long run.


Time is on my side.

TonyC
Nuclear Energy Trader

Total Posts: 1278
Joined: May 2004
 
Posted: 2006-04-24 20:23
dont know who intruduced the idea into the thread, but universal portfolios are NOT about finding a stock that goes up 100% in period "a" and down only 50% in period "b" . . .

. . . the simple two stock case in the original papers had two stocks that both rose over time, but happened to have weak correlation . . . it turns out that the lesser the correlation of the assets, the better off the universal portfolio idea is . . .

flaneur/boulevardier/remittance man/energy trader

LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-24 20:47

TonyC,

It's an example that T Cover and others use (in their more simplified papers) to explain what they do.


Time is on my side.

TonyC
Nuclear Energy Trader

Total Posts: 1278
Joined: May 2004
 
Posted: 2006-04-24 22:47
actually, the simplified example i am familiar with were TWO hypothetical stocks one going from 1 to zero every period, and the other going from 0.5 to zero every other [off cycle to the first stock], period . . . so the stocks had NO return . . .not a single stock that went up 100% or fell 50% for a 50% expected drift . . .

but the klintcher was the example of two real stocks [iraquois brands and ark something?] with real end of day prices etc . . .

flaneur/boulevardier/remittance man/energy trader

LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-25 02:49

In the example that I read (I think you can find it on the web pages of Cover's hedge fund, Mountain Analytics), the volatile stock (if I remember correctly) goes like 1, 2, 1, 2,  .... Or like 1, 0.5, 1, 0.5, ...... Either way, you can obviously pump money from that into the cash account.

My understanding is that Cover showed that an elaborate version of the above pumping procedure can be made to work at the level of the entire market, and he proved that one can systematically form a portfolio that beats any constant rebalanced portfolio (I take that to mean it can beat any single volatile stock).

The assumptions made are that: Every stock is volatile, and more importantly, that you are willing to wait forever. If the whole market fizzles to zero and stays there, Cover's portfolio also fizzles to zero and stays there, but slower than any fixed rebalanced blah, blah, blah.

I still don't know what to make of the whole thing. My understanding is that Pension funds are required by law to invest in portfolios in a certain way. Cover's has a systematically winning portfolio, with very good theoretical properties. Why should the Pension funds use any other?


Time is on my side.

lexx


Total Posts: 60
Joined: Apr 2006
 
Posted: 2006-04-26 23:15
I'm not sure you can apply this concept to the whole market,
it is pretty numerically intensive to get portfolio weights :
http://www.qfrc.uts.edu.au/conferences/qmf2001/Ishijima_H.pdf

One question, since in Cover's original paper, it seems that final portfolio weights are simply weighted by geometric return combination of all possible (feasible) weights. Therefore portfolio that starts to grow fast relatively to others will dominate in final portfolio weights.
Why not form a portfolio, that given historical returns determine weights as those that maximize portfolio's geometric return since inception ?

kr
Founding Member
NP Raider
Total Posts: 3561
Joined: Apr 2004
 
Posted: 2006-04-27 00:32
why should they use any other?

umm, how about:  if it were so obvious and profound, why shouldn't the market have converged to this stable point long ago?

I remain a cynic on this issue - seems like if it were such a sure thing, your ability to magnify the drift through leverage would be unlimited.  I don't see the force that limits this action.

my bank got pwnd

quantie


Total Posts: 884
Joined: Jun 2004
 
Posted: 2006-04-27 01:39
could someone point me to a recipe for this?. i see the original cover paper but no algo in there..

lexx


Total Posts: 60
Joined: Apr 2006
 
Posted: 2006-04-27 06:00

Some discussion on this topic

http://www.hamilton.tcd.ie/events/10Nov2004/Slides.pdf


LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-27 15:30

kr,

The prolem (as I see it) is that all conclusions in this approach are strictly asymptotic. No one tells you that you'll make any profit within a given finite time scale.


Time is on my side.

lexx


Total Posts: 60
Joined: Apr 2006
 
Posted: 2006-04-27 16:01
Another concern associated with Universal Portfolio is how volatile is it? - it may have too low Sharpe ratio.

LongTheta
The Snowman

Total Posts: 3129
Joined: Mar 2004
 
Posted: 2006-04-27 16:24
My recollection is that in his original paper, Cover says that he has no bounds on the volatility. I expect that all such issues were addressed in later works. But I thought more than one person said that the draw downs can be enormous. Now, you can say, I'll invest only a small fraction of what I have in such a UP, but then you won't be able to adequately cover the the market, and may not survive the draw downs.

Time is on my side.

lexx


Total Posts: 60
Joined: Apr 2006
 
Posted: 2006-04-27 16:57
Why would size of investment have any impact - you can cover the market with small-sized positions , no ? Well, probably depends on the minimum number of shares you can trade. From what numerical experiments I have seen number of assets for such scheme would hardly exceed 100, so depends what market you want to cover - DJIA with 30 stocks will be fine, but Russell1000 would be a tad problematic.

quantie


Total Posts: 884
Joined: Jun 2004
 
Posted: 2006-04-27 18:07
i didn't see the isihijima paper below..anyone has any thoughts on the testing...

kr
Founding Member
NP Raider
Total Posts: 3561
Joined: Apr 2004
 
Posted: 2006-04-27 22:05
 we're all dead in the asymptotic...

my bank got pwnd
Previous Thread :: Next Thread 
Page 2 of 4Goto to page: 1, [2], 3, 4 Prev Next