Factorial calculation for drawdowns on grid trading systems. - page 2

Post whatever you need to post until you are all satisfy.

I am not grown up with the mentality of a little kid.

I don't have a need or the urge to satisfy my childish ego.

The best advice I can give you is learn to refrain from emotional breakdown.

Know what makes you tick and then you will realize that you have allow your own self to tick like a fool.

You are your own fault.

Oh Really? No childish mentality?

Or childish ego?

And this is just cherry:

Considering this emotional breakdown:


But don't lose hope!

Wow! I did not imagine that you would constantly reply back.

I guess you want to have the last say or word in everything so you can look good.

Well, be my guess and waste your time posting to your heart's content.

I just love your attitude and the way you pick random sentences from my writing just to look good.

People cannot be that dumb.

Random sentences without the whole topic is an incomplete picture.

Your silliness shows a lot about your childishness.

I have done some research on grid trading and the characteristics of grid and anti-grid strategies, especially drawdown and profit vs. time and vs. price. See here: http://sites.google.com/site/prof7bit/snowball

Short summary: The loss of a grid or the profit of an anti-grid is proportional to n * (n + 1) / 2 where n is the price move in levels. This is a quadratic function. On the other hand the profits of a grid or the losses of an anti-grid grow linear with time. This results in a quadratic relationship between price and time when calculating (or extrapolating) the break-even point. The break-even when plotted into a chart will be a horizontal parabola. For grids the price must stay within the parabolic area, for anti-grids it must leave this parabolic area to become profitable.

There is also a quite sophisticated semi-automatic EA (free and open source) provided to trade the anti-grid with visual break-even calculation and display in the chart, realtime equity plot, profit-projection, pause and reverse, bi- or unidirectional trading modes, auto-start, auto-takeprofit and other bells and whistles.

Let's assume for a second that we can model most price changes on lower timeframes as a random walker; continuing your mathematical analysis:

1. The steps taken of a RW are linear in time, so: n~t
2. The expected distance from origin of a RW (a well known result) is: d~ +-sqrt(n)
3. But the distance is actually d=p-p0, so: p-p0~+-sqrt(n)
4. We introduce a proportionality constant a (such as described in your analysis): n=a*t
5. After substituting (4) in (3) we reach the same result: p=p0+-sqrt(a*t)

Conclusion: asymptotically we expect the price to reach the same parabola that represents the break-even point!!!

Before everybody screams bloody-murder and sacrifices me on the alter of "prices do not behave as random walkers", I'll justify the above intuitively by pointing out the following: there is no 'intelligence' behind both systems (grid and anti-grid); they do not forecast anything and are mechanical by nature; they tend to filter out any non-random part of the signal and latch on to the random part. (IMHO).

Comments:

1. In reality we have to pay to enter the game, hence we have to be further away from the parabola... Since we are expected to reach it, we'll lose eventually.

2. All creative 'tricks' done by so many grid-traders cannot change this expected outcome, since they do not change the asymptotic behavior of the processes involved.

7bit, judging from that analysis u must be a fellow engineer... A mathematician would do that analysis in a completely different manner... Regardless, kudos! It's excellent!

p.s. IMHO both strategies have a negative expected value - in the long run they will lose... Again - IMHO.

Yes, this is the little (important) detail that I (knowingly) suppressed ;-)

This system is not an automated holy grail, it is not profitable in itself.

When trading this anti-grid I am effectively hunting for the black swan that would usually kill the grid trader, when volatility increases for a short period of time and I have to apply some kind of intelligent analysis to find good entry and exit points for starting and stopping the EA.

Having traded this for some time now I have found that most of the importance seems to lie in finding (or waiting for) a good exit: wait until the "abnormal" high volatility starts, watch it, be happy and then exit just moments before it is over and everything reverts to the normal (quasi-random) behavior again. By doing it this way I don't have to predict these events, I just wait until they have already happened and only then I take action.

I have another Idea going around in my head and this would be hedging the losses of a grid with the profits of an anti-grid. Both grids should have significantly different stop_distance values and this should theoretically be able to exploit different roughness (fractal dimension, hurst exponent) on different timeframes. I will do some experiments with this idea soon.

Just don't forget that expected value is linear (see 'Linearity' property of Expected value); combining 2 strategies with a negative expected value cannot produce a positive one (even if it seems that one wins every time the other one loses). Something fundamental has to change in order for this to work. IMHO, if you add actual intelligence/forecasting into this algorithm, it would no longer resemble what it is now - it would not look like 'grid' trading anymore. Anyway, this is just IMHO. I might be wrong of course.

Are you guys traders first and technicians second or technicians first traders second? From what I understand, a true technician does not care about fundamental information and vice-versa. When I look at a price chart, all I'm interested in is price direction and maybe time. How this express mathematically on a grid does not seem relevant. Would you really need to know how many square-roots with in quantum space, moving from point a to b to unlock secrets of the markets? When a technician wrote no money-management scheme could make negative-expectation systems profitable, I just accept as universal truth and move on. I'm trying to follow all this but don't see where it'll apply practical.

I think you cannot simply declare both strategies as losing at the same time, at least they are not losing in the same way, in fact in the scenario that i have in mind it would actually be the grid that is in fact profitable in the long run, just like martingale would be profitable if i only had a source of unlimited capital. The losses of a grid result from the sudden game-over event that happens when (temporary!) drawdowns occur. The source of (temporary) unlimited capital in this case would be provided by the anti-grid just during these black-swan moments, exactly as much as needed and exactly as long as it lasts.

this whole idea is based on the one and only (yet unproven) hypothesis:

• the parabola will be of different width for different grid-spacing and I can find a combination of grid and anti-grid where the parabola of the winning grid lies outside the parabola of the losing anti-grid.
  

This effectively means that price is not an ideal random walk, its hurst exponent is not the ideal 0.5 (random walk). We would then either have more ranging than trending and then the tighter grid would make profits while the wider anti-grid (losing) would provide the insurance for the few black-swan events (at slightly less running costs) or it is more trending than ranging and we would profit from the anti-grid while the grid could pay parts of the running costs of the anti-grid (and in this case I think we could even leave away the grid altogether)

Measurements have shown that the breakeven parabola of the anti-grid will get wider (worse) when the grid spacing is reduced, similarly the breakeven of a grid should (not measured yet) get wider (better) when the grid spacing is reduced. If I can find a grid with a wider parabola than the parabola of an anti-grid on the same instrument then I have the holy grail.

This all is still nothing more than a crazy idea, circulating around in my head. Most likely I will end up finding that while although the effect is indeed there I won't be able to significantly overcome the spread costs, spread will widen my smaller anti-grid parabola and shrink my wider grid parabola back to where they almost meet each other and then I will more or less break even. I will have to do real measurements to find the answer.

Perhaps so, but it's irrelevant. I was not talking about the temporary profits in a fixed period of time, but about the Expected value - the long term profitability of the strategy. The question you should be asking yourself is whether each strategy, if run by-itself, is profitable in the long run (= has a positive expected value). If not, then why would they make a positive expected value when running concurrently? The only way that's possible is if in the first place at least one of these strategies had a positive expected value. IMHO, both don't have it... But even if I am wrong, the linear property of Expected value is universal - the Expected value of running 2 strategies concurrently will be the sum of their expected values if they where running by themselves.

That's a common misconception. If u had a source of unlimited capital the balance graph would be jumping between extreme loss to extreme profits in a zig-zag fashion forever. As human beings it's easy to focus on the part of the graph that has positive balance and claim that all we have to do is stop playing when we are in that position - and since the graph is zig-zagging between loss and profit, we know for sure that it would always come back up. That's true - but there was no reason to focus on the upper part of the graph in the first place... Mathematically we earn nothing - the expected value is zero (the bottom parts of the graph even out with the upper parts of the graph)... Worst, in real life we have to pay to play the game, so the expected value is likely to be negative.

The expected distance from origin of the price for each strategy will be it's own parabola. The tighter the grid, the more (random) steps are taken, hence the RW parabola widens as well. This won't change the underlying asymptotic behavior of the processes (IMHO).

And it almost surely isn't. It's likely that u are right and indeed it behaves more like a biased random walk (hurst exponent != 0.5). But what's missing in this strategy is the element which identifies or forecasts the bias in this RW. Since that element doesn't exist, any non-random element of the signal is ignored and we are left with a strategy that tries to exploit the random part of the signal with a 'martingale-like' strategy... IMHO, that is doomed to fail.

p.s. I think your approach to analyzing the strategy is excellent. Stick to the math...

Edit: a biased random walk does not imply that hurst exponent !=0.5 of course (I don't why I wrote that...).