A truly riskless system?

[dtrader98]

Sambian,

You were kind enough to share some of your ideas, so I'll let you know some observations on your simulation that I believe are flawed.
First off, I'm no expert on Forex, but it appears your conversion ratios are backwards. For instance, you have 1/2 the dollar amount on Fcell
multiplied by usd/eur ratio (cell c(n)) to get euros (cell e(n))? It should be multiplied by eur/usd (b(n)) to convert to euros. Unless I'm very wrong, this is a major error. And there are similar other conversion errors as well.

Secondly, I'm starting to understand some of the other arguments regarding paths made thus far. You simply assume one binary uniform random variable which is eur/usd and invert to get usd/eur. That is not a good way to model the real behavior, for one it misses the intermediate paths to get to double or half. For two, it ignores the dependency on the underlying instruments. The better method would be two generate two independent random walks for eur and dol, then ratio the resulting indexes relative to those results. If you make the random walks gbm/gaussian, you'll find that the net re-balancing scheme is no better than a random walk itself (i.e. not riskless at all).

You started out with some very good seeds, but unless I'm missing something, I don't think the end result was anything spectacular.
If you get a chance, try the above and see if you agree or disagree.
I appreciate your sharing your ideas though, you are on to some good ones.

 

[MathAndLogic]

Quote from sambian:

It might seem unrealistic, but it is true. If the price follows a random walk, the probability of an up movement to x is equal to a probability of a down movement to 1/x.


Ok, now think about this example:
I offer you a game, in which we flip a fair coin. You pay me some amount of money to participate in each flip. If it comes up heads, I give you back twice your bet, and if it comes up tails, I keep half of your bet. How much will you bet each time?
For example:
You have $10. You believe that the Kelly ratio should be 1 and bet all - you pay $10 for the first flip. It comes up heads and I pay you back $20. Then you bet them all, the coin comes up tails and I keep half of your bet, so you are left again with $10.

In this situation the Kelly formula gives f* = 0.25, therefore you should risk $2.5 in the first coin flip. The optimal bet is to bet half of your money each time, and the same logic is used in my article.

For example:
You have $10. You know that the Kelly ratio is to bet half of your money and pay $5 for the first flip. It comes up tails and I keep $2.5. Then you bet half of your $7.5 = 3.75, the coin comes up tails and I pay you back twice your bet, so you are left with $11.25.

The problem here is your random walk model. I think you are mixing continuous processes with discreet ones. In your model, each step of the random walk is 1. If each step is that big, everyone will make money. You flip a fair coin that has two discreet events and you get paid more than you lose, even though it is random whether the outcome of each flipping is head or tail. You have positive expectancy.

But if you really want to talk about random price movement, you must use much smaller steps, like one pip (0.0001) instead of 1. In this case, price goes up or down by 0.0001 instead of 1. You will find that the price will cause you more losses than you have appetite for. In other words, it is much much much harder for a random walk whose steps are of size 0.0001 to reach your winning price target than a walk with step size of 1 (10000 times larger).

In your original article, it is unrealistic to use 1 for the movement of EUR/USD. Let's make an analogy in the spirit of your original article. You start at 0, and set your profit target at 1 and stop loss at -0.5. If each step of the move of EURUSD is of magnitude 1 and each step for USDEUR is 0.5 (let's not even talk about the problem with linking 2 variables here), then it is very easy to make money. But if you make the random walk of step size 0.0001, then you will realize the probability of loss is far greater. Let me simplify this even more. Consider an asset X priced at 0, and you set profit target at 1 and stop loss at 0.5. Now consider the following 2 situations:

(A) X is uniformly and randomly distributed between -a and a, a>=1. With each passing unit of time, you are give a value of X between -a and a. You have positive expectancy.

(B) X moves randomly up or down by an infinitesimal step and makes one move with each passing unit of time from its previous location. In this case, the probability of X hitting your stop loss in any period of time overwhelms the probability of X hitting your profit target in the same period of time.

Bypassing the numerous tiny little steps X needs to make is your critical flaw. Reality is represented by (B), and your model is represented by (A).

It is simple to verify the above by either mathematical proof, but I think it is best if you could convince yourself by running a Monte Carlo.

Regards,

M&L

 

[sambian]

Quote from dtrader98:

Sambian,

You were kind enough to share some of your ideas, so I'll let you know some observations on your simulation that I believe are flawed.
First off, I'm no expert on Forex, but it appears your conversion ratios are backwards. For instance, you have 1/2 the dollar amount on Fcell
multiplied by usd/eur ratio (cell c(n)) to get euros (cell e(n))? It should be multiplied by eur/usd (b(n)) to convert to euros. Unless I'm very wrong, this is a major error. And there are similar other conversion errors as well.

There are no errors.
If you have some amount of dollars = x and want to buy euros with half of it, how much euros can you buy? It's either (x/2)/eurusd or (x/2)*usdeur.
For example:
You have $4. eurusd = 2, usdeur = 0.5. How much euros can you buy with 4/2 = $2? Obviously the answer is 1 euro. To get that number, you have to multiply $2 by usdeur = 0.5.

Quote from dtrader98:

You simply assume one binary uniform random variable which is eur/usd and invert to get usd/eur. That is not a good way to model the real behavior, for one it misses the intermediate paths to get to double or half. For two, it ignores the dependency on the underlying instruments. The better method would be two generate two independent random walks for eur and dol, then ratio the resulting indexes relative to those results. If you make the random walks gbm/gaussian, you'll find that the net re-balancing scheme is no better than a random walk itself (i.e. not riskless at all).

I think that what you write here has nothing to do with reality. Euro and dollar by themselves don't follow random walks, because they don't have any value alone by themselves. Euro and dollar have values only when compared to something else. If I ask you now what is the value of the dollar, what number can you give me? You can't give me any number, you can only give me the price of the dollar against the euro, or against the gold, or against the S&P etc.
So the price ratio of eur/usd might follow a random walk, but not the euro or the dollar.

Anyway, if you can make a random walk as you understand it on Excel and send it to me, I can show you that my system will be profitable, if your random walk is really random.

 

[sambian]

Quote from MathAndLogic:

The problem here is your random walk model.

Ok, if you can make a random walk as you understand it on Excel and send it to me, I can show you that my system will be profitable, if your random walk is really random.

Quote from MathAndLogic:

Let me simplify this even more. Consider an asset X priced at 0, and you set profit target at 1 and stop loss at 0.5.

(A) X is uniformly and randomly distributed between -a and a, a>=1.

I'm worried that your examples include prices of 0 and negative prices, which is impossible in the real world.

(B) X moves randomly up or down by an infinitesimal step and makes one move with each passing unit of time from its previous location. In this case, the probability of X hitting your stop loss in any period of time overwhelms the probability of X hitting your profit target in the same period of time.

Bypassing the numerous tiny little steps X needs to make is your critical flaw. Reality is represented by (B), and your model is represented by (A).

I'm worried that you assume that "an infinitesimal step" down is equal to "an infinitesimal step" up. But "an infinitesimal step" down is equal to 1/(1+"an infinitesimal step" up).

Anyway, send me your random walk model on Excel and I'll tell you what I think about it.

 

[dtrader98]

Quote from sambian:

There are no errors.

Yes, you are right, I misread the tables. Thank you.

Anyway, if you can make a random walk as you understand it on Excel and send it to me, I can show you that my system will be profitable, if your random walk is really random.

Fair enough, pm me where to send it.

 

[Random.Capital]

Quote from sambian:

I am the author of the article to which you posted a link.

The Euro has been in existence for approximately 8 years. It has yet to reach either of your "50%" probabilities. Assuming you laid that position on the day the Euro started trading, and the Blessed Event miraculously happened tomorrow morning, your compound rate of return (of the "expectation") would have been ~2% p.a.

I'll leave the practical numeraire difficulties to one of our more verbose posters.

 

[MathAndLogic]

Quote from sambian:

Ok, if you can make a random walk as you understand it on Excel and send it to me, I can show you that my system will be profitable, if your random walk is really random.


I'm worried that your examples include prices of 0 and negative prices, which is impossible in the real world.


I'm worried that you assume that "an infinitesimal step" down is equal to "an infinitesimal step" up. But "an infinitesimal step" down is equal to 1/(1+"an infinitesimal step" up).

Anyway, send me your random walk model on Excel and I'll tell you what I think about it.

The range from -a to +a is just an example. If you are concerned about 0 or negative numbers, just translate [-a, a] to [2a, 0]. Start your random walk at 1, set your profit target at 2 and stop loss at 0.5.

 

[Random.Capital]

Quote from SomeYoungGuy:

This is a simple Martingale Mean Reversion strategy.

And that is yet another problem. If the Blessed Event happened on meaningful timeframes, the risk of ruin in this approach is very high. It will eventually lead to being flat-out broke.

 

[slapshot]

OK, all of you smart people can flame me now. I am just a guy who draws a few lines on a chart with no other indicators and then trades the tape based on how price acts near those lines. I barely graduated high school.

But it seems to me this whole thread has been an exercise in "static" mathematical academia and not in practical trading theory.

1) you will never see Euro vs. USD or any combo above mentioned at 100% or even 50% gains or losses down to 0% or any of the other premises of the system

2) you have made no allowances for comissions, spreads, slippage, mistakes, not being available to execute at the exact levels described, power outages, etc. etc. etc. etc.

3) you assume a perfect static fill price at exactly your chosen percentages each time you convert back/forth - this is totally unrealistic due to emotions, doubts, hesitations, etc. etc. etc.

OK, blast my face off now.

 

[epetrov]

Quote from SomeYoungGuy:

At the risk of stepping on sambian's toes, I will take a stab at it.

The Sambian Strategy (as I will now call it) doesn't work like that. It doesn't take a point in time and decide what to do, it watches price (without regard to the time it takes to move) and makes a decision to rebalance the accounts when price hits one of two thresholds.

I agree that sambian system is not like that, but we can try the modification - adjustments on equal time periods - for example on weekly.