In Nature, random mutations may be both good and bad. So in some sense, you could think it's a zero-sum game. There's no progress because the number of things improved by the random mutations is the same as those that worsen. However, this argument is wrong because of natural selection. The successful mutations spread while the unsuccessful ones die out. As a result, it is a positive-sum game, not a zero-sum game, and life has been doing progress.

Now, how to reformulate this simple observation due to Darwin so that you earn those billions? It's simple.

For the sake of concreteness, imagine that you trade currencies. Well, you trade the eurodollar. You're able to leverage the motion of the rates by the 100-to-1 ratio. So if the rate changes by 0.01%, you lose or or gain 1%, depending on the direction.

Imagine that you have two accounts (of the same initial value) and you make the opposite bets with each of them. Well, then you lose as much as you gain. The result is zero. But that's only when you don't change your original positions.

But now imagine that you do readjust both positions so that the leverage remains 100-to-1. There exist more efficient ways to do so but a mechanical rule is that you simply reinvest the extra profit if you're making the profit or you're closing a part of your position continuously if you're losing so that the effective leverage remains 100-to-1.

Is that possible? A special discussion should be done whether approximate schemes to achieve it are good enough.

The point is that with this reinvestment strategy, the total value of each position will depend as a power law – will really exponentially depend – on the exchange rate. If the exchange rate at time \(t\) is\[

E(t) = E(0)\cdot \kappa,

\] with a positive \(\kappa\), then the value of the positions that were betting on the increase or decrease of \(E(t)\) will be\[

W_i\cdot \kappa^{100}, \qquad W_i\cdot \kappa^{-100},

\] respectively. One of them was exponentially growing, the other was exponentially converging to zero. You might think that they cancel but they don't. For example, if you had $1 and $1 to start with and the exchange rate changed by the factor of \(\kappa=2^{1/100}\sim 1.007\) so that \(\kappa^{100}=2\), then one of the positions doubled the value and the other halved it.

You will end up with $2 and $0.50, respectively. The sum is $2.50 i.e. 25% higher than you started with, regardless of the direction of the motion. At some moment whose timing may either be fixed and pre-programmed or it may depend on the state of your account, you may close your positions with a 25% profit.

For example, you may close the positions every time when you achieve this 25% profit. Then you invest your new money symmetrically to both directions again.

Because the rates change by 0.7% every other day or so, you multiply your wealth by 25% every two trading days. There are about 200 days like that in a year which means that you add 25% about 100 times a year, increasing your wealth by the factor of\[

1.25^{100} = 5\times 10^{9}.

\] So if you have one dollar, you will have about 5 billion dollars after one year. 500 billion percent annual yields are slightly higher than what many banks offer you in their checking or saving accounts. In three years, if the naive maths will hold ;-), you may finally build the galactic-size collider. Now, before you start to mechanically realize this procedure, you should check: isn't there a simple error in this idealized calculation? Is it possible to maintain the 100-to-1 leverage? And if this thing works, won't the spreads kill you? In the real life, you will lose something by trading too often so you are

*forced*to replace the idealized description above by an approximation because you simply can't afford to trade too often.

You optimize the moment at which you should close your positions and the accuracy with which you try to emulate the exponential growth. The question is For how many PIPs of spread – the punishment of transactions – you may still show that the procedure that approximates the algorithm above is profitable?

Was this post left over from April 1?

ReplyDeleteThe betting phases don't change your net worth, and neither do the re-balancing phases, so how can a sequence of them do so?

You should try your hand at robo trading, Lubos, then we can rename you

ReplyDeletethe "Plzeň Whale." That'll give me a

chance to squid you with a

harpoon.;~)

http://octophant.us/m/posters/CephaLovePod.jpg

I think that what you will find is that the spread (bid vs asked) will prevent success to all but the best funded trading programs.

DeleteMy favourite entrepreneur is giving $ 25 millions to whoever comes up with economically reasonable

ReplyDeletesuggestions to lower carbon emissions.

http://www.spiegel.de/international/business/richard-branson-discusses-climate-change-business-opportunities-a-839985.html. . :-)

Hi Lubos,

ReplyDeletearen't you tacitly assuming that EURUSD is following a previsible process? If it is stochastic, you can only benefit from portfolio adjustments already made.

Let's say EURUSD follows a process with independent stochastic increments dS_t. Denote the rebalanced net position at time t by N_t. The expected return of the position will be E [ N_t dS_t | F_t ], which is conditioned on the information F_t available at time t (the filtration of the process). I can take N_t out of the expectation value because it is known at time t (it is F_t-measurable, by construction). The profit is N_t E [ dS_t | F_t ]. In a risk-neutral world, this expectation must equal the risk-free rate. There is no profit above the risk-free one...

Best,

Tobias

Ignoring the transaction costs, would it still work if everybody were using the same strategy? Would the fastest computer trading system win?

ReplyDeleteSpeaking of squid, the Vampire Squid, that is, (Gordon will know what

ReplyDeleteI'm talking about), why the

hell is this important story in Rolling

Stone only in the midst of 100 great guitar riffs?

http://www.rollingstone.com/politics/news/the-scam-wall-street-learned-from-the-mafia-20120620?print=true

That should tell you volumes about the complicity and overwhelming crookedness within the MSM.

And speaking of guitar riffs, here's David

ReplyDeleteGilmour performing one of the greatest guitar riffs in the history of rock:

http://www.youtube.com/watch?v=3duAGTJ_QJI

Great! Someone will use this strategy (or some other new fangled monstrosity) to make a billion dollars. Soon other heavy-hitters will figure out the game (thanks for making it public knowledge) and start playing it too. Next thing you know the whole market overshoots in one direction or another and "bang!", another crisis on top of the ones already in play.

ReplyDeleteMaybe the Mayan's were right?

Dear Luke, quite generally, strategies can't work for everybody. The only question is what exactly goes wrong. If people were using superlong exposures, it would accelerate the motion of the rate. This strategy is one of the nasty destabilizing kinds. If everyone were doing it, the rates would be running to infinity or zero. However, there would be other regulating forces in the market. At some moment, you would lose the people who can make the transactions with you.

ReplyDeleteThis will quite clearly not work. Try to describe precisely how your leveraged portfolio would be constructed, what does it mean to take "opposite" positions in the context of currencies, and what are the currencies that your W's are in, and you will realize that such a "risk-free profit" strategy will not work, even in a frictionless world without any limits on positions or trading costs.

ReplyDeleteI am almost certain you must be right. But could you please be more specific what fails to work in the method?

ReplyDeleteGordon: Ok, I am trying a post. When I connect with, say, facebook, it posts my full name. If I post like this, I cant get my avatar. Is there an edit for the avatar.

ReplyDeleteAnyway, I don't need a trading scheme when I own one of these :) :

http://travel-wonders.com/2011/02/05/photo-of-the-week-one-trillion-dollar-note-zimbabwe/

Dear Gordon, you haven't even registered with DISQUS, so you obviously can't change the default avatar yet. You must register with DISQUS, the "D" square-shaped icon, and then you may edit both your displayed name as well as the avatar.

ReplyDeleteFor starters, forget about leverage because that does not play any role. Just focus on what it means to take opposite positions.

ReplyDeleteThink about EUR/USD, and start with E_0 = 1 (EUR/USD). I am a USD investor and want to "speculate on the exchange rate". I take 1 USD and turn it into 1 EUR. At time t, I receive 1/E_t USD back.

But what does it mean to take an opposite position? It means that I take 1 EUR and turn it into 1 USD, and at time t, I still have 1 USD, or, if I exchange it to euros, I have E_t EUR.

So I end up with 1/E_t + 1 USD, or E_t + 1 EUR. This is certainly not a risk-free profit.

The problem in your example is that your two W_i's are in different currencies. Once you convert one of the portfolios to the same currency as the other, you get the values I stated in the previous paragraph, and you can't exploit the symmetric feature that you suggest.

Come on, your comment seems to be a misunderstanding of the forex trading in general. All such leveraged positions mean that one owns a much larger positive number of one currency and a large negative amount of the other currency. It is not true that one only owns one of them.

ReplyDeleteNo, leverage has little (nothing) to do with the argument. Start with 0 USD and borrow 2 million USD (i.e. infinite leverage), half of which you exchange into EUR. Do the same with the millions of EUR and USD, instead of just one EUR and one USD. You end up with 1 mil * (1/E_t + 1) USD from your trade, minus two million which you need to return = 1 mil * (1/E_t - 1). This can be positive or negative, depending whether E_t < 1 or E_t > 1. No risk-free positive return.

ReplyDeleteDamn, the posts don't show up...

ReplyDeleteNo, leverage has little (nothing) to do with the argument. Start with 0

USD and borrow 2 million USD (i.e. infinite leverage), half of which you

exchange into EUR. Do the same with the millions of EUR and USD,

instead of just one EUR and one USD. You end up with 1 mil * (1/E_t + 1)

USD from your trade, minus two million which you need to return = 1 mil

* (1/E_t - 1). This can be positive or negative, depending whether E_t

< 1 or E_t > 1. No risk-free positive return.

I have no idea if my replies are posted - I get the message "you have already made this comment" but the comment does not show up...

ReplyDeleteAnother try...

ReplyDeleteNo, leverage has little (nothing) to do with the argument. Start with 0 USD and borrow 2 million USD (i.e. infinite leverage), half of which you exchange into EUR. Do the same with the millions of EUR and USD, instead of just one EUR and one USD. You end up with 1 mil * (1/E_t + 1) USD from your trade, minus two million which you need to return = 1 mil * (1/E_t - 1). This can be positive or negative, depending whether E_t < 1 or E_t > 1. No risk-free positive return.

I see lots of your comments. They're surely visible. Thanks for the calculations. They must be right because my conclusion was absurd. Will look at it when I am less busy.

ReplyDeleteLubos, as a practitioner I'd be happy to go into more detail offline. I assumed this was a joke when you wrote it, but evidently not. Basically there are two flaws, the first is that the stochastic process you are describing isn't a Martingale. The second is that leverage and shorting don't work the way you are assuming.

ReplyDeleteIt was partly a joke. Still, I have some problems to understand why you don't simply write the explanation and/or the corrected formulae as a comment instead of these confusing "demos". Are the corrections you would offer me in private secret?

ReplyDeleteJust two points: levarage amplifies losses as much as gains - and the bank, your creditor, does not want to take any risk at all. I.e. as soon as you lose 1 dollar on your 100 dollar portfolio, it issues a "margin call", asking you to provide more capital. If you don't, they liquidate your full portfolio, leaving you with exactly zero dollars. Maybe you did not incorporate this non-linearity into your model...

ReplyDeleteSecond point, your system is unlikely to work, because... there is enormous quantity of (arguably) very smart people thinking how to beat the system and make money. It is plausible that all trivial systems were alrady discovered and employed, i.e. have already beaten themselves to death. Mostly this happened by someone finding some market inefficiency (opportunity caused by imperfect distribution of information among market players) and by exploiting it, killed it and made the whole system more efficient...

Just my (unleveraged) 2 cents...

I find the partnership of Dick Rutan and Richard Branson very curious. When Branson makes comments like, "we have to stop climate change." It only proves he hasn't got a clue of what he is talking about. I guess it just proves that even an idiot with a good idea can make money.

ReplyDeleteMy first reply didn't show up, but I said Branson is proof that even an idiot with a good idea can make money. Here is more proof he is an idiot:

ReplyDeletehttp://www.nationalreview.com/planet-gore/303790/rio20-showdown-richard-branson-david-rothbard#

Dear woodNfish, I added you to the white list. Sorry for the nonsensical messages about "abuse" for the first time - everyone gets that, a DISQUS messaging bug. You shouldn't see them again.

ReplyDeleteThanks Lubos.

ReplyDeleteI like Pink Floyd. I've been listening to them for over 40 years, but I like this too:

ReplyDeletehttp://www.youtube.com/watch?v=MXp413NynFk I think Santana is one of the greatest guitar players ever.

A futures contract is an agreement between two people who are called "counter-parties". The agreement is that one of them will give the other a sum on a certain day (US style). The sum depends on some external thing for example the price of the Euro or Microsoft. If you sell your contract early, then someone else steps into your shoes (or your counter-party buys back the contract from you). You can't make money going long and short the same future's contract because you'd be making the contract with yourself and you can't make money from yourself.

ReplyDeleteThe other trading agreement is the "option". An option gives someone the right to purchase or sell something on or before a certain day (the "expiration date") at a certain price, (the "strike price"). By "certain" I mean that the date and dollar amount are included in the contract and do not change. A "Call" option gives one the right (option) to buy something at the strike price. "Put" options give one the right to sell something at the strike price. These rights are only valuable if the market price is above (for a call), or below (for a put) the strike price at th expiration date.

Purchasing a put and a call leaves one in a position where one loses money if the underlying asset price ends near the strike price and making money if it ends far away. One can definitely lose money this way. On the other hand, buying a call and selling a call is just like taking two sides of a future's contract, there's no way to make money from yourself.

It is an interesting fact of trading that all trading agreements can be described in terms of a (possibly infinte) number of futures contracts and options contracts. The exponential behavior is built into the options contracts as they either expire worthless or valuable.