Financial natural selection: how to easily earn billions of dollars

A typical TRF reader has tens of millions of dollars and is somewhat bored. A half of those would like to transform the millions to billions. It's easy, just read and follow these instructions. By doing so, you promise that you will send your humble correspondent 1% if you earn big bucks and you won't hold him responsible for your failure if any.



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?