6 ms·

You don;t necessarily have to be able to spot the trick to know there is one. If you know that the expectation value of any combination of bets is just the sum

You don;t necessarily have to be able to spot the trick to know there is one. If you know that the expectation value of any combination of bets is just the sum of the expectation values of the original bets, you'll know there cannot be a way to combine zero-expectation bets to get a positive expectation. Because no matter how you sum up zeroes, you'll end up with zero.

saurik 4y ago
I recommend watching this lecture, as the effect here isn't magic or fake: it is just a tradeoff of how you manage your portfolio to convert volatility into return and there is a ton of well-studied math relating to how it works. https://youtu.be/8TJQhQ2GZ0Y https://youtu.be/8TJQhQ2GZ0Y And like, yes: there is a moment in the lecture where he explicitly sets up a scenario where the expectation value of your bets sums to zero and yet the rebalancing makes money. It isn't a free lunch, of course: if the two assets both go down and stay down then you lose money, and you don't gain as much money as you'd want on the way up; but if they are both sputtering around you definitely make money. If you were to somehow be able to rebalance infinitely fast it also doesn't make money; and yet, it only makes money in relationship to the volume you are able to rebalance, so there is another tradeoff. At the end of the day you can thereby model it as making money by providing the service of "providing liquidity" to the market, and what you are effectively doing is taking a spread on that as a market maker.
- s1artibartfast 4y ago
  Is it just a fancy Martingale then?
  - Dylan16807 4y ago
    A Martingale that you can do with finite money sounds pretty nice on the surface.
    - s1artibartfast 4y ago
      You can Martingale with finite money too.
      - Dylan16807 4y ago
        How? Google isn't helping.
        s1artibartfast 4y ago
        The martingale strategy increases just shifts the risk around. Your typical (not average) bet becomes profitable, but a string of bad luck becomes catastrophic. You double your bet each time you loose, so you have a better chance of making back to your losses, however, you increase your chance of loosing everything to an unlikely event. https://en.wikipedia.org/wiki/Martingale_(betting_system) https://en.wikipedia.org/wiki/Martingale_(betting_system) You can do it with any amount of money, but it still isn't long term profitable unless you have an infinite bankroll.
        Dylan16807 4y ago
        I thought the wording was clear, but I meant doing it with no chance of getting stuck in an error state. Finite money can't properly implement a martingale. It can implement this strategy.
        s1artibartfast 4y ago
        Both are simply strategies with downsides. This strategy is just as broken. Properly applied to betting it goes broke in the long run too. it is identical to proportional betting, a strategy that makes no money on average with an infinite bankroll, and will eventually bankrupt you with a finite one. The description is also flawed in the blog. If anyone offers you a 50/50 bet to win $50 or lose $33,take it. Given that it's posted by financial advisors , The blog is probably intentionally misleading
  - saurik 4y ago
    I do not see the connection, unless you are just talking at some useless-ly high level of "a trading strategy that isn't guaranteed to win" (though the way in which it fails isn't at all the same: it isn't that you go insolvent but that you made the wrong bet about the correlation of the assets), but that's me being extremely uncharitable and so maybe you are seeing something I am not. The mechanism is essentially unrelated, the goal is somewhat different, who does it is certainly different (at this is the core of market making and portfolio diversification, so smart people do this all the time)... I just don't see why you are saying that unless you are just trying to trivialize the result (but again: this is me being extremely uncharitable, so please push back if you are onto something).
    - s1artibartfast 4y ago
      I am trying to trivialize the result, although much of it is targeted at the broken and wrong example of the blog. It talks about rebalancing between two assets. For a gambler this could simply be the bet and the bankroll. (this is the example used in the blog). (ignoring the fact that the blog is playing a +EV game) what was described is "proportional betting". The short term outcome is a normal distribution with a mean of zero. Like the martingale, If you run it to infinity, you will always go broke. for proportional betting, the failure mode is a string of bad bets taking the bankroll below minimum bet size (the long tail on the normal distribution). When we talk about real world trading, the whole idea of "shannon's demon" is trivial. In the zero growth case, it assumes the mean value is known and constant so it just boils down to sell high, buy low.
      - cyanydeez 4y ago
        In the absence of any "new information" the market is believed to be a random walk. And before the information age, the market likely did act like this. But now adays, the dark pools, random subreddit s, etc, almost guarantee that a ticket will fluctuate a price incoherently. So to find the mythic mean is probably impossible. But the demon could be generate via a novel method of analysis, which definitely wouldn't be presented here, as knowing the method would invalidate mythic mean.
    - 4y ago
Schroedingersat 4y ago
There's no trick in the analysis. Only in the axioms. If you have two assets that really do have zero expected return but vary independently, it's trivial to see that moving equity from the one that went up to the one that went down (or went up less) will net you a return. The 'trick' if you will is that there aren't actually any uncorrelated assets.
- beagle3 4y ago
  What you wrote is only true under additional conditions (e.g. mean reverting processes). In the i.i.d case, you are wrong, even if items are correlated.
- v0idzer0 4y ago
  What about inversely correlated assets? Still correlated but presumably would work for this just the same. Bull vs bear ETF on the same security should bring near perfect inverse correlation.
- imtringued 4y ago
  As others said the asset itself has a baked in return but let's entertain it for a bit. Effectively what the article is describing are speculative profits that can only be made by switching between two assets. The obvious result is that trading between the two assets will reduce their volatility and hence correlate them. The profits that you can make here are the usual kind of volatility premiums that any normal daytrader earns.
ouid 4y ago
The expectation of the original game is quite positive. You can see this visually by rescaling the first graph.

saurik 4y ago

I recommend watching this lecture, as the effect here isn't magic or fake: it is just a tradeoff of how you manage your portfolio to convert volatility into return and there is a ton of well-studied math relating to how it works. https://youtu.be/8TJQhQ2GZ0Y https://youtu.be/8TJQhQ2GZ0Y And like, yes: there is a moment in the lecture where he explicitly sets up a scenario where the expectation value of your bets sums to zero and yet the rebalancing makes money. It isn't a free lunch, of course: if the two assets both go down and stay down then you lose money, and you don't gain as much money as you'd want on the way up; but if they are both sputtering around you definitely make money. If you were to somehow be able to rebalance infinitely fast it also doesn't make money; and yet, it only makes money in relationship to the volume you are able to rebalance, so there is another tradeoff. At the end of the day you can thereby model it as making money by providing the service of "providing liquidity" to the market, and what you are effectively doing is taking a spread on that as a market maker.

s1artibartfast 4y ago
Is it just a fancy Martingale then?
- Dylan16807 4y ago
  A Martingale that you can do with finite money sounds pretty nice on the surface.
  - s1artibartfast 4y ago
    You can Martingale with finite money too.
    - Dylan16807 4y ago
      How? Google isn't helping.
      - s1artibartfast 4y ago
        The martingale strategy increases just shifts the risk around. Your typical (not average) bet becomes profitable, but a string of bad luck becomes catastrophic. You double your bet each time you loose, so you have a better chance of making back to your losses, however, you increase your chance of loosing everything to an unlikely event. https://en.wikipedia.org/wiki/Martingale_(betting_system) https://en.wikipedia.org/wiki/Martingale_(betting_system) You can do it with any amount of money, but it still isn't long term profitable unless you have an infinite bankroll.
        Dylan16807 4y ago
        I thought the wording was clear, but I meant doing it with no chance of getting stuck in an error state. Finite money can't properly implement a martingale. It can implement this strategy.
        s1artibartfast 4y ago
        Both are simply strategies with downsides. This strategy is just as broken. Properly applied to betting it goes broke in the long run too. it is identical to proportional betting, a strategy that makes no money on average with an infinite bankroll, and will eventually bankrupt you with a finite one. The description is also flawed in the blog. If anyone offers you a 50/50 bet to win $50 or lose $33,take it. Given that it's posted by financial advisors , The blog is probably intentionally misleading
- saurik 4y ago
  I do not see the connection, unless you are just talking at some useless-ly high level of "a trading strategy that isn't guaranteed to win" (though the way in which it fails isn't at all the same: it isn't that you go insolvent but that you made the wrong bet about the correlation of the assets), but that's me being extremely uncharitable and so maybe you are seeing something I am not. The mechanism is essentially unrelated, the goal is somewhat different, who does it is certainly different (at this is the core of market making and portfolio diversification, so smart people do this all the time)... I just don't see why you are saying that unless you are just trying to trivialize the result (but again: this is me being extremely uncharitable, so please push back if you are onto something).
  - s1artibartfast 4y ago
    I am trying to trivialize the result, although much of it is targeted at the broken and wrong example of the blog. It talks about rebalancing between two assets. For a gambler this could simply be the bet and the bankroll. (this is the example used in the blog). (ignoring the fact that the blog is playing a +EV game) what was described is "proportional betting". The short term outcome is a normal distribution with a mean of zero. Like the martingale, If you run it to infinity, you will always go broke. for proportional betting, the failure mode is a string of bad bets taking the bankroll below minimum bet size (the long tail on the normal distribution). When we talk about real world trading, the whole idea of "shannon's demon" is trivial. In the zero growth case, it assumes the mean value is known and constant so it just boils down to sell high, buy low.
    - cyanydeez 4y ago
      In the absence of any "new information" the market is believed to be a random walk. And before the information age, the market likely did act like this. But now adays, the dark pools, random subreddit s, etc, almost guarantee that a ticket will fluctuate a price incoherently. So to find the mythic mean is probably impossible. But the demon could be generate via a novel method of analysis, which definitely wouldn't be presented here, as knowing the method would invalidate mythic mean.
  - 4y ago

Schroedingersat 4y ago

There's no trick in the analysis. Only in the axioms. If you have two assets that really do have zero expected return but vary independently, it's trivial to see that moving equity from the one that went up to the one that went down (or went up less) will net you a return. The 'trick' if you will is that there aren't actually any uncorrelated assets.

beagle3 4y ago
What you wrote is only true under additional conditions (e.g. mean reverting processes). In the i.i.d case, you are wrong, even if items are correlated.
v0idzer0 4y ago
What about inversely correlated assets? Still correlated but presumably would work for this just the same. Bull vs bear ETF on the same security should bring near perfect inverse correlation.
imtringued 4y ago
As others said the asset itself has a baked in return but let's entertain it for a bit. Effectively what the article is describing are speculative profits that can only be made by switching between two assets. The obvious result is that trading between the two assets will reduce their volatility and hence correlate them. The profits that you can make here are the usual kind of volatility premiums that any normal daytrader earns.

ouid 4y ago

The expectation of the original game is quite positive. You can see this visually by rescaling the first graph.